Can a PA bank's loan department withdraw loan payments out of a customer's bank account without their verbal authorization?

It depends on the written agreement. Read the note that was signed and it should state if offset is allowed. Usually it depends on what type of loan you are talking about too.

Thank you. I'm assuming offset occurs only if the customer holds a checking account at the bank of the lender. Correct?

I am assuming you are dealing within your bank for the offset. Your deposit agreement can also state offsets concerning the deposit account and offset from dealings within your bank.

Look at both the loan and deposit agreements for the correct language for your bank offsets.