Yes, the state return can be filed anytime between now and the extended deadline of October 15.
If you are not filing a Federal extension, then you will need to print and mail Form REV-276 by May 17, including a payment for any taxes owed to the state.
See the following TurboTax article for more details and a link to the form you need to file for PA:
Do I need to file an extension for my personal state taxes?
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