I entered personal property tax paid during my federal return but my state return is not asking for personal property paid in order to deduct it from my state taxes owed.

Generally when you enter this in the Federal portion of your return, it will carry over to the state if there is a related credit. What state are you working on?

Thanks for your reply, I am working on a South Carolina return.

It's always good to enter all your tax payments (like personal property tax) into your Federal return, even if you're claiming the Standard Deduction.

 

Since South Carolina starts their tax calculation with the Federal Adjusted Gross Income, there is no option to use either the Standard or Itemized Deduction. 

 

So there is no place to enter a personal property tax amount in the South Carolina return; it's already taken from the federal return AGI.

 

Here's more info on Itemizing Deductions in South Carolina.