So let's look at Andrea's thought process for a second here.
A) The governor is dead
Ok, it's not necessary to do anything to his car. Nor could you really use it unless you went to get his keys.
B) The governor will survive
Andrea is on the other side of a large building. By the time she gets to the vehicle, he could already be there, or he could catch up to her while she's slashing tires. It's not a very smart move unless she was armed to defend herself.
Seems like she made the right choice to me. If she went back and he caught her there, people would probably be complaining about that too.