I am filing my Kentucky State Taxes and I owe them money. Do I have to send in a voucher with the payment? I downloaded the program on my computer so it is not online.

Yes if you efiled your return.  Or you can probably pay directly on the state website.  Doesn't make any difference if you used the Online version or the Desktop program.

I did not efile my return.  I am mailing everything together and just need to know if I have to have a voucher payment with it.

More info:

If filing a paper return, complete Form 740-V and send it and your payment in the same envelope as your paper income tax return. Do not staple Form 740-V or your check to your return or to each other.

Turbotax completes the form for you.