Do I need to pay MA state taxes on distributions from a 403B, that have previously been taxed by NJ at the time of contribution to the 403B?

Does the info in <a rel="nofollow" target="_blank" href="https://www.mass.gov/service-details/view-other-states-tax-treatment-of-out-of-state-government-pensions">https://www.mass.gov/service-details/view-other-states-tax-treatment-of-out-of-state-government-pensions</a>  apply in your case?

I just read the MA DOR info that you pointed me too and I don't think it answers the question I have.  The link you provided only talks about pensions; specifically, state government pensions.  I believe a 403B is a federal retirement plan program, similar to 401K but, seems to allow states to include contributions in taxable income, as opposed to how federal reduces taxable income at the time of contributing.  Does this MA DOR information also apply to return of 403B contributions that have already been taxed in another state?  I am trying to avoid the cost of hiring a CPA for this but, the answers don't seem to be easily found.  

As I see it, New Jersey has assessed the all contributions for NJ Income tax at the time of earning, irrespective of the fact that the same contributions are at the Federal level deferred compensation and not taxed until withdrawn from the savings plan.

Massachusetts, instead, defers assessment on both the employee and employer contributions until such time as withdrawn.

"Distributions made to you from the 403(b) plan are excluded from gross income if such distributions represent Massachusetts previously taxed contributions.  Distributions in excess of Massachusetts previously taxed voluntary contributions before January 1, 1998 are taxable"
https://www.mass.gov/service-details/view-government-pensions#403

Apparently you retired or otherwise ceased to continue participation by contributing after relocating to Massachusetts.  Just in case that is incorrect and you did make contributions when a Mass. resident  that distributions made to you from the 403(b) plan are excluded from Mass. gross income if such distributions represent Massachusetts previously taxed contributions.

Several key points:

1. A resident of NJ having relocated from Massachusetts and then receiving pension distributions does not  have a total reciprocity discussed in this article following.  Massachusetts allows a deduction for some or all of the distribution depending on the other state's (NJ) treatment of MA pensions:
   New Jersey All out-of-state government pensions qualify for the pension exemption:
   For the 2018 tax year in New Jersey, if you are 62 or older and make less than $100,000 per year, you can exclude up to $45,000 of pension, IRA or annuity income if you are a single person. Married and civil union couples filing jointly can exclude $60,000, and those filing separately can exclude $30,000.
   https://www.mass.gov/service-details/view-other-states-tax-treatment-of-out-of-state-government-pens...
   https://www.state.nj.us/treasury/taxation/njit7.shtml
   
   
2. Enacted in 1996, the Pension Source Act (P.L. 104-94) prohibits the states from taxing pension income of non-residents, even if that pension was earned in the non-resident state,
   
   
3. Massachusetts generally follows the rule for calculation distributions from a qualified retirement plan in which you have "basis" - that is already taxed monies. The distributions become taxable after exhausting the basis - such that it is only the generated income within the plan that is then taxable, but there must be a valid accounting.  So, that said, the question to which there seems to be neither a MA DOR TIR or other statement is:
   Since all the basis was of non-Massachusetts earning income, should that basis be treated in a similar fashion?
   I would argue yes and that would mean that in the MA Form 1 or Form 1-PY/NR interview you would indicate that basis in the calculation of what is taxable in the distribution.

From what you wrote, this is probably redundant, but note that a non-resident of Massachusetts is not subject to tax on pension distribution https://www.mass.gov/info-details/learn-about-tax-treatment-of-pensions-in-massachusetts#nonresident...  as this reiterates the (P.L. 104-94).

I think you do have to pay tax, but that is just my interpretation of the instructions for Form 1.  Read the instructions, specifically, for Line 4 of Form 1:

"If your pension is not exempt, you should generally enter in line 4 the taxable amount reported on your U.S. Form 1040, line 16b, or U.S. Form 1040A, line12b. In some cases, however, Massachusetts law requires an adjustment to the federal amount. Distributions from annuity, stock bonus, pension,profit-sharing or deferred payment plans or contracts described in Sections 403(b) and 404 of the U.S. IRC must be adjusted to account for your contributions that have been previously taxed. Subtract from such income (as reported on your U.S.Form 1040, line 16a, or U.S. Form 1040A, line 12a) the amount of your contributions which was previously taxed by Massachusetts until the total of your taxed contributions is received. If your pension falls into this category, enter the adjusted amount in line 4. "

I have bolded the relevant sections.  It appears that you can only exempt your basis in the 403 (b) plan if the basis arises because the contribution was previously taxed by Massachusetts, not another jurisdiction.  This is the same sort of double-taxation that a MA taxpayer faces because IRA and solo 401 (k) contributions are not deductible from MA income at the time of contribution, which creates a MA tax basis, even if there is no federal basis.  If the MA resident moves to CA, for example, they would still owe CA taxes on the withdrawal, because there is no CA basis.  In your case, you have no MA basis so there is nothing to exempt from your MA tax return. 

I will ask another MA Superuser to weigh in on this.

Thank you so much for your efforts and assessment.  It is pretty much the same as what I gleaned from the research I have done on this.  I do appreciate you asking another MA Superuser to get another opinion on this as, being double-taxed on my hard earned money is something that I would really like to avoid if there is any possible way to do so.  I look forward to seeing what another Superuser thinks.  Thanks again.

Unfortunately, the answer while probably beneficial is not simple. See answer

My read from the links provided is that if the 403(b) is, indeed, paid out as an annuity contract, then, according to the link I first cited, the first $20K ($10K for single taxpayers) is deductible from MA income.

That is the NJ 2018 exclusion, for singles, which you had not mentioned.
Again note that per Federal law the pension is not taxable in MA unless MA earnings were contributed.

If I may make a practical suggestion: instead of proactively hiring a CPA, as there seems to be a reasonable reading that you can exclude, go ahead and exclude the relevant NJ amount cited earlier and let MA decide if it wants to take a different tack.

Thanks to all of you who have weighed in on this issue. I have decided to consult with a MA cap in mid-May.  After I find out what can be done, I will revisit this post and post what transpired.

Go for it.  The one other, off the wall, suggestion your CPA can consider is whether you can claim a credit against MA taxes on the same income taxed by NJ in an earlier year.  It would be interesting, indeed, to be able to attach an old NJ return to a current MA return to show the tax paid.

That would only apply if the taxpayer while contributing the NJ pension was working in MA with MA-sourced income and as a result may not have been able to exclude that contribution.  This is extremely unlikely.

As earlier said, the Federal law pretty much asserts the inability of Massachusetts to in arrears assess tax on the out-of-state pension into which out-of-state sourced income was contributed.

I would like to see a resolution on this question.  I have the same problem in the other direction, leaving MA to retire.  It is incorrect that MA does not tax 403(b) contribution at time of contribution.  I am paying now on my 403(b) contributions.  (It is correct, as above, that the only Mass. regs I can find refer to "pension" contributions, but mine is not a pension ("optional retirement program," alternative to pension).)  I am worried about double taxation, i.e., not being credited with my MA payments at time of contribution, when I retire to a different state and take distribution, especially if the state, unlike NJ, does not tax at time of contribution.