Firefighters are being called to false alarms more than once a week on average at the University Hospitals Coventry And Warwickshire NHS Trust, new figures show.
Figures from NHS Digital show the fire and rescue service were called out to false alarms 57 times in the 12 months to March.
According to the National Fire Chiefs Council, false alarms are a growing problem and are a “considerable drain” on fire and rescue service resources.
They could pose a risk to safety by diverting firefighters away from genuine emergencies or by causing complacency towards what could be real alarms, it said.
Paul McCourt, from the NFCC, said: “False fire alarm activations cause huge problems for the NHS and the Fire and Rescue Service.
“Every year thousands of staff hours are lost due to false alarms and Unwanted Fire Signals.
“This affects both fire and health service delivery, business continuity and patient care.”
Fires broke out on 1 occasion over the course of the year, but nobody was injured.
Across England, the number of call-outs to NHS trusts rose by 8% last year from 6,533 in 2016-17 to 7,065 in 2017-18.
The majority of false alarms are caused by automatic systems, which may summon the fire service as soon as they activate.
Most are caused by faulty, damaged or badly maintained systems, or things such as burnt toast, steam or dust.
Sara Gorton, from the health workers union UNISON, said it was “yet another example” of underfunding in the NHS.
“False fire alarms are not only disruptive for staff and patients, but also pose a risk to their safety,” she added.
“It’s time the government acted to address the rising backlog of repairs affecting trusts.”
Since 2011 fire services have the power to charge non-domestic premises - including NHS sites - if they are persistently called to false alarms because of faulty automatic fire alarms.
In 2014, the London Fire Brigade began issuing hospitals and other properties with a £295 fine for every false alarm after the first nine in a 12 month period.
The Brigade said at the time it hoped the charges would encourage those responsible for offending buildings to improve the maintenance of their alarms.
It has since discontinued the practice, however.
Mr McCourt continued: “NFCC asks that local NHS organisations contact and work directly with their local fire and rescue services who are able to help and advise on how best to address the growing problem of false alarms and Unwanted Fire Signals.
“By working together on the management and maintenance of fire alarm systems we can deliver the best possible services to the public without increasing costs or down time.”
A spokeswoman for NHS Improvement said: “All NHS hospitals take fire safety seriously.
“This includes following national fire safety regulations which require them to maintain their automatic fire detection systems.
“We would expect all NHS trusts to put measures in place to minimise the number of false fire alarms, while ensuring the safety of patients and staff.”