The automatic stay applies to both husband and wife while the bankruptcy case remains open, even if the wife did not file. It's better to be safe than sorry!
I have to respectfully disagree. The Chapter 7 filing only protects the husband and not the wife. Since the car is already repossessed then you will not have to lift the automatic stay. If the husband filed a Chapter 13 then you would have to wait until he defaults on the 13 plan and it gets dismissed before pursuing the wife.
Attorney Badwan is correct. If only one spouse filed a chapter 7, then the automatic stay which stops any collection action including a lawsuit applies only to the spouse that filed the chapter 7. In a chapter 13, non filing co debtors are covered by the stay as long as the chapter 13 case remains open.
This answer is provided for informational purposes only. Actual legal advice can only be provided in an office consultation by an attorney licensed in your jurisdiction, with experience in the area of law in which your concern lies.
As you have indicated after having done your research, the co-debtor stay does not apply to a Chapter 7 filing. Thus, you may proceed with suit against the wife.