My rmd distribution from my 403b are taxable in the state of New York.how do I submit it on my 1040?

What is the TurboTax phone number? (intuit.com)

After you enter the 1099-R in the federal income section and answer a couple of questions that income will transfer to the NY return automatically.   Complete the state interview later then review the return before filing.

Did you get the 1099R for it?  

Enter a 1099R under
Federal Taxes on left
Wages & Income at the top
Then scroll way down to Retirement Plans and Social Security
Then IRA, 401(k), Pension Plan Withdrawals (1099-R) – Click Start

Don't type the bank name or try to import it.
At the bottom pick - Change How I enter my Form
Then on the next screen pick - I'll Type it in Myself

Be sure to pick the right kind of 1099R on the 4 boxes. 1099R or CSA1099R or CSF1099R or RRB1099R
If you are filing a Joint return be sure to pick which person it is for.

Be sure to answer all the follow up pages to the end of that section.