Investigators say that purse was snatched from a vehicle parked outside Handels Ice Cream in Berwyn in late November.
Within the next few days, the woman began depositing stolen or counterfeit checks into that victim's account. With the checks deposited, the thief would then go to other branches and withdraw money.
"The banks where my victim's name and identification were used are all over the place," said Chief John Haggerty of Easttown Police.
Police say they have very few leads, saying the woman appears to covering her tracks.
They believe she uses rented vehicles to commit her crimes. The license plates were removed before the vehicles came in range of bank cameras, police said.
"She was using two different vehicles. Both vehicles are brand new. One is a Tahoe, the other is an Expedition and, on both occasions when these banks were hit, there were no tags on the vehicles," said Chief Haggerty.
Police have connected the woman to at least one other car theft in the King of Prussia area.
Detectives believe she may be part of a larger organization. Earlier this month, Upper Merion police busted up a criminal ring committing similar crimes along the Route 202 corridor. Police don't yet know if this suspect is part of it.
"I'm not sure at this point, it looks like it is. Our victim obviously doesn't know this woman in these surveillance pictures we've been passing around," said Chief Haggerty.
Investigators say they do not know if the suspect is from the area. If she's not, police say they may never see her again.