Do I need to file an extension if I DON'T owe taxes, but can't file by the deadline today?

No, but it's a good idea just in case!  https://turbotax.intuit.com/irs-tax-extensions

Hi kmccoy-

You do not need to file a federal extension if you don't owe taxes but it wouldn't hurt in case you do up owing (avoid penalties) see the below article for state specific information.

https://ttlc.intuit.com/questions/1899449-how-do-i-extend-my-state-in-turbotax-easy-extension