TurboTax produces an IRA Information worksheet. Worksheets are for your info, and are not sent to the IRS. If you have been using TurboTax (TT) continuously since you started making Roth IRA contributions, the current year worksheet will have a your total Roth IRA contribution basis and conversion basis. The worksheet for each year you did a return will have your contribution for that year.
You are expected to keep ypur own records, but your financial institution may be able to provide it. You will only need that information if you make an early (non qualified) withdrawal. Qualified distributions are entirely tax free, so you need that info.
