If I made a rollover contribution to my IRA account from another retirement account of mine, do I need to report this in some way?

Yes, if you have a Form 1099-R for the rollover you will enter it into TurboTax. Please see Where do I enter my 1099-R? In the follow-up questions you can indicate it was a rollover.

If it was a trustee-to-trustee transfer from one IRA to another IRA and you do not receive a Form 1099-R then you do not need to report it on your return.