Tax impact of a Roth distribution paid back within 60-days

I would advise you not to change from the codes that you have on your 1099-R. That is what is being reported to the IRS, and your changing it in TurboTax doesn't change what the IRS will receive.

Instead, do this:

Report the 1099-R as it was written, then choose Continue. Keep continuing through the section, until you reach the screen: What Did You Do With The Money From This Payer? 

Select: I moved the money to another retirement account (or returned it to the same retirement account). and:

I rolled over all of this money to another Roth IRA (or returned it to the same account). (see screenshot) 

You will then see a screen:  We Want to Let You Know....You won't have to pay tax on your $10,000.00 rollover from This Payer.Check these rules to make sure you qualified to roll over your IRA.

Continue through all the rest of the section to complete reporting this rollover.

Code J is correct if you were under age 59½ at the time of the distribution.

Thank you both for the assistance.  My concern about reporting that I had rolled over the withdrawal was that it will actually occur in 2016 and I'm reporting my 2015 taxes.

This whole issue has become less convoluted because after more research I discovered that I can withdraw any contributions I've made to my Roth tax and penalty free; only the earnings would be taxed prior to 59 1/2.  I will not even be required to repay the withdrawal to avoid a penalty, unless I simply choose to do so, because my total amount of contributions since 1999 are in excess of the amount I withdrew.  This is clarified on line 22 of Form 8606.

True.  But if your goal is to maximize the long-term benefit of the Roth IRA, you'll probably want to do the rollover.

The only requirement is that the rollover be completed by the 60th day after the day of the distribution.  There is no requirement that the rollover be done before the end of the year in which the distribution occurred (provided you are still within the 60 days).

What if the rollover is slightly over 60 days?  We bought a home for our son with Roth IRA (basis) funds, but the home equity loan we applied for took a little longer than 60 days to go through.  

The RULE is 60 days period ... you cannot miss by even a single day.  Now it is treated as a distribution and is subject to taxes, penalties and interest if applicable.  

 I don't believe you qualify for a waiver of the penalty (if you have any with a ROTH) but here are the instructions:  

Revenue Procedure 2016-47 enables individuals to self-certify that they are eligible for a waiver of the 60-day deadline and complete a late rollover.

1. Double check the status of every rollover you attempt. Don’t assume one has been completed just because you did your part. Mistakes happen. You can’t correct a mistake you don’t know about, and a delay hurts your case with the IRS.

2. See if the reason that your rollover wasn’t completed within 60 days is on the list of 11 circumstances the IRS says may justify a waiver. Examples: financial institution mistake, postal error, death in the family. For a complete list and a copy of the IRS’ sample letter, visit: https://www.irs.gov/pub/irs-drop/rp-16-47.pdf

3. If the reason for the delay is listed, write a self-certification letter and send it to the administrator or trustee of the employer plan or IRA that is receiving the rollover. Don’t send it to the IRS. The IRS provides a model letter in the Revenue Procedure, and requires that it be followed on a “word-for-word basis or by using a letter that is substantially similar in all material respects.”

4. Complete the late rollover as soon as possible after the problem that caused the delay is remedied. The IRS provides a “safe haven” period of 30 days that it deems acceptable.

5. Prepare to be audited. The IRS will know of the late rollover because it will be reported on Form 5498 by the financial institution receiving it. In the Revenue Procedure, it says “a copy of the certification should be kept in the taxpayer’s files and be available if requested on audit.” After an audit, the IRS may still deem you ineligible for a wavier. You may or may not be audited, but remember the high stakes and be ready to justify your position if you are.

Mamadesiete, that's the risk you take when you take a distribution from an IRA to provide the equivalent of a short-term loan.  The 60-day deadline and the one-per-one-year-period limitation on rollovers were enacted specifically to discourage such use of IRA funds.  When IRA distributions have been used in this manner, the IRS has invariably denied requests for waiver of the 60-day deadline except perhaps in one case I recall where an escrow company made some mistake that delayed the funds beyond what was explicitly promised.  In the exception case the taxpayer filed for a Private Letter Ruling requesting waiver of the 60-day deadline, but recent changes to the fee structure make requesting a PLR  prohibitively expensive and, in your circumstances, almost certainly would be unsuccessful anyway.  Revenue Procedure 2016-47 does not provide any relief under these circumstances; the situation you describe does not conform to one of the permitted reasons for self-certification. 

The distribution is not taxable if the distribution consisted only of Roth IRA contribution basis (although it is reportable), but you've lost the potential for future tax-free growth on that money.