In general, if you have your name on the title of a car and are considered a co-owner then you have vicarious liability for the actions of anyone who operates the vehicle. So if as a co-signer you had your name placed on the title and/or registration of the car then likely you will be considered a co-owner and thus could be sought after if the other co-owner / main driver was in an accident and caused damages.
If you are not listed on the title but only are named on the loan then your risk of being involved in legal matters are not as great since you only signed to make payments or be financially responsible for the vehicle if the primary signer defaults or fails to make payments timely.
This is just general information and we would advise you to contact an Arizona lawyer that is familiar with AZ liability laws and civil suits regarding auto accidents to see what liability you would have in your position as a co-signer on a loan for an automobile on which some else is the main driver.
As a co-signer of a car loan it is important to make sure the primary user of the car has car insurance on it and with high enough limits that they would not be exceeded in an accident and leave the driver and any car owners listed on the title at risk for being sued in a civil suit. To make sure the primary keeps insurance on the car see about being added as an additional insured on the policy so you will be informed if the policy is changed, cancelled, etc.
Get a for Arizona insurance quote from an auto insurance specialist here.