The group calls itself "Robin Hood of Keene." Members walk city streets with rolls and dimes of quarters to feed the meters.
WMUR-TV reports the city accuses the group of interfering with officers' work. It asks them to stay at least 50 feet away.
The group records its time outside and posts videos online, sometimes showing members following the officers.
The city says one officer suffered stress, anxiety and heart palpitations from the group's actions.
Group member Garret Ean says he's not trying to cause any medical problems. He says he tries to keep a good demeanor with all the parking meter enforcers.