Unfortunately, the asnwer depends on the specific situation in each individual case. What's important is that one needs to know the rules and play by the rules. This is called bankruptcy planning.
First, it depends on whether your car is paid for or whether you are still making payments on it. That is, a preliminary issue is whether there is any "equity" in your car. Thus, the first question you should ask yourself is: how much is my car worth? You can look up your car's value at after bankruptcy, the bank can go after you not only for the car, but also for any deficiency that is likely to be there after the bank repossesses the car. By contrast, if you don't sign a reaffirmation agreement, as long as you continue to make payments on the car, the bank will probably leave you alone. Notice that I said "probably," because technically the bank in most cases has the right repossess your car based on the mere fact that you have filed for bankruptcy (based on a clause in your purchase contract signed when you bought your car). Thus, it all depends on what risk you are willing to take. Some people do not like to take even a very small (de minimus) risk. From experience, most people are ok with simply making payments on their cars without signing a reaffirmation agreement, but everyone's situation and risk-aversion are different.