When I download my tax returns they are unsigned. There's nothing to indicate they were electronically signed. How do I obtain a signed copy of my return?

[VolvoGirl]

There is not a signature on them.  If you need to give someone a signed copy you need to sign it in ink yourself.   If you efiled there should be an Electronic Postmark page. Probably near the end. That is your proof and signature. 

[Critter-3]

IF you used the "online" software

and

IF you log into the exact same Online account you used to file prior year taxes

Then, you can download a NEW PDF copy of the prior year tax return from your online account, open that PDF and look for the sheet called "Postmark Report" 

...that sheet contains both the submission time/date, and the acceptance date