Sheller, 27, said that she had asked the officers to wait until someone could come to get them, but that the officers refused and even laughed about it.
Sheller's father, Center City lawyer Stephen Sheller, who owns the car, didn't think it was all that funny.
He and his daughter are suing the Police Department and the Parking Authority, arguing that the officers violated the department's rules when they left the couple on the street.
The lawsuit, filed this week in Common Pleas Court, also alleges that the live-stop law is unconstitutional.
"The law is clearly illegal," Stephen Sheller said. "It doesn't take a rocket scientist to see that. It amounts to an unreasonable seizure, and they shouldn't be getting away with it."
Lt. Raymond Evers said the Police Department could not comment on pending litigation.
Sheller and his daughter are seeking an injunction against the law, as well as restitution and damages for themselves and others whose cars have been towed under the statute.
Live-stop was implemented in parts of the city in 1998 as an effort to keep illegal drivers off the streets and possibly to help lower Philadelphia's high auto-insurance rates. In 2002, the law went into effect citywide.
Thousands of cars are impounded under live-stop each year - close to 23,000 in 2010 alone, Evers said.
The guidelines regarding speeding tickets or other such infractions give police officers the freedom to make judgment calls, depending on each situation. But the law states that police officers must impound any unregistered cars, Evers said, as well as vehicles driven by anyone with an invalid or suspended license.
"We don't allow officers to use their discretion," Evers said.