Do I have to catch up on car payments if I want to keep my financed car in bankruptcy?

Maybe.  

In a chapter 13, no.  When you file a chapter 13 case, you can put your auto loan into your chapter 13 plan and start making payments through the chapter 13 trustee  (more below).

In a chapter 7, 99% of the time, you will have to be current on payments eventually if you want to reaffirm and keep the loan (more below).

Chapter 13

In a chapter 13 case, you file a plan with the court.  In this plan, you start making monthly payments to the chapter 13 trustee, who then makes payments to various creditors.  Your car loan will be part of this plan.  It does NOT matter if you are current on car payments.  Even better, your payments won’t start until next month.

For example, let’s say that you file a chapter 13 today.  You stop making car payments immediately (or maybe you already stopped).  Your first chapter 13 plan payment will be due on the 25th of next month.  As of this blog, today is March 8th.  If we filed a chapter 13 today, you would start making plan payments (including the car payment) beginning April 25th.

Chapter 7

In a chapter 7 case, if you want to keep a car loan, you reaffirm the debt.  You can find reaffirmation elsewhere in the blog, but basically, you sign a new agreement to pay the same balance, interest, and payments on your car.  99% of the time, the creditor will NOT let you reaffirm unless you become current on the car loan.  That doesn’t mean that you need to be current on the day you file your chapter 7, but in the next 2-3 months, you need to catch up on those missed payments.

If you are behind 2-3 months into the chapter 7, they will definitely repossess the vehicle, and you will  not be able to reaffirm.