I amended my NY state return because I overstated my NYC resident income since I had moved out of NYC.
Do I have to send in a federal amended return or can I just e-file the NY amended return?
If the changes that you made on the New York return do not affect the Federal return, there is no reason to file a federal amended return.
After you make the changes in NY, I would compare the federal you filed to what the federal says now.