Can I garnish someone's income tax if I have a garnishment judgement?

Ordinarily, a garnishment is filed against a bank or employer. You would have to file your garnishment against the U.S. Treasury Department and the IRS; I have never heard of this being done; and they may be exempt from garnishment.

I'm not sure. Generally only government agencies can garnish one's income tax refund to satisfy a judgement.

I do not know of any way someone else can get someone else's tax refund unless it is to attempt to catch up on back child support. And if that is the case, then the guy, or gal should have been paying the support all along and then they wouldn't have to worry about it at all.

Yes you may, here is some info ( from the court in Mich with thire forms)

http://courts.michigan.gov/scao/courtforms/garnishment/mc52.pdf

MOWERMAN2468 agrees: this could be, but an individual can obtain back child support through tax refunds.Yes, courtesy of the government agency that handles child support collections and distributions for the particular state.