They differ in meaning.
Questioning has negative connotation. It implies that she caused the accident if the police were "questioning" her about it. The police suspect that she caused it. People use "question" like this all the time. For example:
"I question whether he really does have a PhD." It means, I suspect that he doesn't have a PhD.
"The soccer team's poor performance called their coach's qualifications into question." It means, the soccer team plays so poorly that the coach is suspected to be unqualified.
"Asking" has neutral connotation. The police may or may not suspect that she caused the accident. Perhaps she was just watching, and they are asking her about it. If this was the case, you would never say that the police were questioning her about it.