The state of PA is saying I owe them taxes for 2015. I did no live in PA. I did my taxes through turbo tax and I have the documents to prove it.

[xmasbaby0]

Did you WORK in PA during that year, by chance?  Did an employer report earnings for PA to the state?

[Hal_Al]

You owe PA tax and must file a PA state return, if you have PA source income. It does not matter where you live**.

The general rule is: your report all your income on your home state return, even the income earned out of state. You file a non-resident state return for the state you worked in and pay tax to that state. Your home state will give you a credit, or partial credit, for what you paid the non-resident state.

** The exception is if you work in PA, but live in a "reciprocal" state ( Indiana, Maryland, New Jersey, Ohio, Virginia, DC or West Virginia).  

No PA state taxes are withheld or due and you do not normally need to file a return for PA. But  your home state will tax you on your PA income.

If PA state taxes were mistakenly withheld, you then have to file a return, for the PA, to get a refund. Your home state will not give you a credit. You should ask your employer to stop withholding so you don't have to file a PA return every year.