We are in the middle of a divorce. My husband wants to file turbo tax and get the refund direct deposited into his own account. He has used turbo tax in the past and I never signed anything. Do I not need to agree to this tax return filing. How can the government hold me responsible without my signature?

You must agree to file joint return. Also on the paper copy of the return that you keep for your record, both must sign.
If your husband files joint return and you do not take any action, you will be held responsible. So you should tell your husband that you are filing separate tax return.