If you entered the W-2 information on your state tax return before you efiled it, there is no need to send a copy of the W-2 to the state. All the information they need is in the efiled return. The only reason you would need to send a copy of a W-2 is if you printed and mailed your return instead of efiling it. Not sure what happened in prior years. 

You cannot attach copies of your forms W-2 to your NY tax return if you e-file.

And when you e-file, you are not required to attach copies of your forms W-2.

Yet I have been asked to send in scanned w2s for the last two consecutive years by New York state. I was wondering if there were a way to preempt... 

Just by printing and mailing your return with the W2s instead of Efiling.

Similar with my State of KY because I have extra withholding and they must not believe what my e-file says. So they want copies of W-2 and 1099Rs. It would be nice if there was a way to attach a PDF with efile. Certainly can't tell the State no when they ask for verification.

You only need to enter or import the information from your W-2 into TurboTax in order to e-file.

Many individual states have opted to spot-check some W-2's for additional validation, and some are also checking a sample of individual returns for additional identification verification. In some cases, the IRS asks for additional information to establish identity. These are decisions made by the individual tax agencies.

TurboTax allows you to upload documents to your account, but the e-file process doesn't allow for transmission of those documents, just the electronic tax returns.