Can hospital judgments in the US take your income tax return?

In some cases, yes. If the hospital is affiliated with the federal government (ie, a VA facility) your federal tax refund may be offset for any outstanding medical debt. In some states, a state or county owned facility may offset refunds issued from state tax returns. Also money owed on state run programs such as Medicaid and food stamps can be used as offsets on state refunds.

Generally, however, if none of the above apply, the only way a hospital can obtain your tax refunds is to get a court order to attach the bank account where the refund is deposited. In that way, they can intercept any funds deposited into that account and apply it towards outstanding debt, but they cannot directly offset the return.