The group from Stroud, Gloucestershire, are concerned about the location of the masts which will be used in the £2.9bn project to upgrade the Airwave radio system.
Resident Susan Trevett asked a high court judge to overturn planning permission for aerials in her area.
If the challenge succeeds, the contract for the police network might have to be reconsidered.
Ms Trevett's lawyers told Mr Justice Sullivan, sitting in London, there were fears about potential health risks from the antennae.
They also cited reports from the Lancashire branch of the Police Federation which said 173 officers had reported falling ill after Airwave was introduced.
The county was one of the first places in Britain to adopt the service.
Microwave dishes
Outside court, Ms Trevett's solicitor Richard Buxton said: "These masts are being installed with no more than lip service being paid to residents' concerns over possible health risks."
The site of immediate concern to Ms Trevett was near her home on the roof of Stroud police station.
A 13-metre mast with antennae and two microwave dishes is scheduled to replace the old aerial.
In court, David Wolfe, appearing for Ms Trevett, said she was challenging a decision to allow planning permission for new telecom equipment on three separate sites.
Appeal proceedings
Initially, Stroud District Council refused planning permission for the mast because of concern over the potential health risks, said Mr Wolfe.
But it later withdrew its opposition and did not take part in the appeal proceedings before a planning inspector, who allowed the appeal and gave permission for the masts.
Mr Wolfe argued the inspector failed to consider the public health concerns of local residents.
There was particular anxiety because the police station site was close to four infant classes and six junior school classes, he said.
The hearing continues.