Can a rent-a-car business press criminal charges against me for failure to return property?

Only prosecutors can bring criminal charges. You likely can include your financial debts to the rental car company in your bankruptcy. But you can't just keep the car because you've declared bankruptcy, because it was never yours to begin with. The short answer to your question is that you can be criminally prosecuted for failing to return a rental car and it doesn't matter whether you've declared bankruptcy against the rental car company or not.