My husband took out a loan in his name only against our car. My name is on the title also? Is that legal in MN for a bank to give him a loan without my signature? It is in Minnesota.

Did the bank put a lien on the title? Unless the loan is specifically secured by a lien against the title, then it doesn't matter. If a lien was filed, its not that it is illegal, but the lien may only be able to be enforced against his share of the car.