Do you have to report a 1099-R that says "Copy C: For Recipient's Records"

Yes. 

Didn't you also get a Copy B and Copy 2?  Just report one of them 1099R.  

It doesn't matter what copy of the form you have, it needs to be entered on your tax return. Since you have copy "C", there was likely a copy "A" and "B", but they would all report the same information.

Enter Form 1099-R one time regardless of how many copies of the same form are received.

 

Here's how to enter the information on your Forms 1099-R:

 

In TurboTax Online, under Wages and Income:

 

1. Go to  IRA, 401(k), Pension Plan Withdrawals (1099-R)
2. Answer Yes on the screen, Did you get a 1099-R?
3. If you land on the screen, Review your 1099-R info instead, select Add Another 1099-R
4. Answer any questions until you get to the screen, Let's import your tax info. Here you can choose how you want to enter your 1099-R
5. If your financial institution is a TurboTax 1099 partner, you can import your form.
6. Select your institution from the list and enter your sign-in credentials, then select Get my form to start the import process
7. If you prefer to upload your 1099-R or type in the info yourself, select Change how I enter my form. On the next screen, select your preferred entry method
8. Continue answering the questions to enter or review the info from your 1099-R

See this help article for more information.