Please accept my condolences on the loss of your mother, as well.
The IRS states, in Signature on page 4 of IRS Publication 559, Survivors, Executors, and Administrators,
"If a personal representative has been appointed, that person must sign the return. If it is a joint return, the surviving spouse must also sign it. If no personal representative has been appointed, the surviving spouse (on a joint return) signs the return and writes in the signature area “Filing as surviving spouse.” If no personal representative has been appointed and if there is no surviving spouse, the person in charge of the decedent's property must file and sign the return as “personal representative.”"
[Bolding mine based on your question.]
In Your signature(s) on page 35 of New York's Instructions for Form IT-201, meanwhile, it's stated that "If the return is for someone who died and there is no surviving spouse to sign it, print or type the name and address of the person signing it below the signature." See also Deceased taxpayers on page 43 of the New York instructions.
Yes, you're correct, New York prefers that returns be e-filed, but doesn't mandate it except for professional tax preparers.
You might also find the TurboTax Help articles Can I e-file a tax return for someone who is deceased? and Can I file Form 1310 in TurboTax? helpful, as well.
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