You do not have to furnish any proof with your tax return. You only have to furnish proof if the IRS asks for it. They will want to confirm the date of the distribution and the date of the closing to show that the closing was within 120 days after the distribution. The closing date will be on the closing documents. The Form 1099-R for the IRA distribution does not show the date of the distribution, so you would need to have a confirmation or statement that shows the date. As Carl said, they will also look at the closing document to see that the amount you paid at the closing is at least as much as the distribution.
After you enter the 1099-R in TurboTax, and after you enter any other 1099-Rs that you have, continue through the interview. You will get to a screen that asks whether you used the money for one of the things that qualify for an exception to the penalty. When you enter the amount in the box for first home purchase, TurboTax will fill out the necessary form (Form 5329) and include it in your tax return.
