If your federal return could not be e-filed you cannot e-file your state return either. They will both have to be filed by mail.
New York prefers e-filed returns, but there are certain circumstances that make it necessary for you to file your NY return by mail and the state DOES allow mailed returns. If you could not or did not e-file your federal return then your NY return cannot be e-filed. It has to be mailed. It is not possible to e-file any state return if the federal return was not e-filed and accepted by the IRS.
https://www.tax.ny.gov/pit/efile/efile_mandate_for_individuals.htm
https://www.tax.ny.gov/pit/file/return_assembly_mail.htm