You should still be able to e-file NY, but the forms may not be ready yet. Also, If you mailed the Federal return, then the State return cannot be e-filed. It would have to be filed by mail, too.
To check form availability (Personal) in NY see the table below:
https://ttlc.intuit.com/replies/3319879
To check form availability (Business) see the table below and scroll down to NY: https://ttlc.intuit.com/replies/3319878