A neighbor backed into my car while I was parked in the street, and consequently pushed it backward a couple yards. It did not skid; it rolled backward, and damage to the front bumper is superficial. Is there a potential for transmission damage? It is an automatic.

 

Welcome to the forum

Are you certain it rolled and didn't skid?
I am not familiar with the Cobalt's front wheel drive transmission, but as I understand it, in rear wheel drive transmissions there is a small paw or parking sprag that engages when placed into park to keep the transmission from freewheeling away.
The sprag is held in by spring pressure, and I would imagine it could be overcame with the right amount of pressure (this is why the parking brake should always be used, even in auto transmisisons)
Did it harm the transmission, I don't know, but I wouldn't think so in the functioning sense of drive-ability, however I would be concerned about parking it on any inclines from now on...

 

Thank you for your input. I am fairly sure that it rolled when it was pushed- the tire marks go straight back on both sides. He was in a truck and since the damage is minor, I assume that he was going relatively slow. He seemed to have not noticed once he hit it and continued backing up, which makes me wonder if there was much resistance. Which leads me to believe that it rolled.