No, you don't need to provide any proof of your state tax withholding when you file your Maryland return electronically. The process is supposed to be paperless for most people.
There are a few Tax Credits that require you mail in some documents. If that were the case for your tax return, it would be made clear in the TurboTax program that you have to mail them.
If the Maryland DOR can't verify your tax withheld using their electronic records, they will contact you, so be sure to keep a copy of your tax return and W-2 forms for at least 3 years.