Did you itemize deductions last year?
If so, each of you is technically responsible for putting half that amount on your return.
You might point that out to her, and maybe she will sign the check then.
If you did not itemize, you don't have to put it on the return, but perhaps she will sign it if you throw some cash her way?
You might also contact the state with an explanation of your problem, and perhaps they will issue separate checks?
If not, get a judge to make her sign it.
Snipes