Other allegations included vehicle theft, possession of controlled drugs, public fear, alarm and distress, theft by an employee and threats to kill.
A Freedom of Information request has revealed West Mercia Police and Dyfed-Powys Police were called to investigate 167 alleged incidents in the last three years.
The most common call-outs were for theft, public order offences and common assault.
Several incidents were linked to people on drunk or on drugs, and happened at peak times, including Friday nights and weekends.
Most call outs were to the Royal Shrewsbury Hospital, which reported 95 incidents in the past three years, while according to today's figures none were recorded at Princess Royal Hospital in Telford.
In 2012, officers were called to Robert Jones and Agnes Hunt Orthopaedic Hospital in Oswestry for allegations over possession of weapons, sexual assault of a male aged 13 and over and burglary.
Last September, a report of interfering with a motor vehicle was also recorded at RSH, while at Whitchurch Community Hospital allegations of public fear, alarm and distress and assault were made in April and August last year.
Police chiefs said today crimes in hospitals were particularly upsetting for victims already going through an already difficult time.
Officers do include hospitals in their regular patrols across the county, as well as other public buildings.
Chief Inspector Tom Harding said: "Crimes committed within hospital grounds can be particularly upsetting for victims at what may be a significant time of difficulty for them already.
"No matter where a crime takes place we will ensure it is investigated appropriately and we do include hospitals, and other public buildings, within our regular patrols.
"There is also specific legislation that we can enforce regarding public order offences at hospitals due to the severity of the offences. "
Nationally, figures revealed the shocking total of offences that have led to some of the busiest health centres placing officers on site.
A recent investigation found the police are being called about crimes every 10 minutes.
Figures show officers deal with more than 60,000 crimes in hospitals across the UK every year - and the number has risen in the last 12 months.
The number of offences is so high that several police forces, including Greater Manchester and Lancashire, have started basing liaison officers at some of the busier A&E departments.
The true scale of the problem is likely to be much higher as the figures only represent two-thirds of Britain's police forces and do not include the biggest, the Metropolitan Police.
A total of 30 forces responded to a Freedom of Information request, which shows they attended 64,728 calls to hospitals and other NHS premises in 2013 - a rise of almost 1,700 on the previous year.
Greater Manchester Police attended 12,726 incidents on NHS premises last year - an increase of 320 on the year before.
Officers in another of the UK's larger forces, West Midlands, attended 7,132 calls to hospitals and other health premises in 2013 - up 249 on the 2012 figure.
Police chiefs are warning that those who threaten or assault NHS staff will be dealt with robustly.
The Royal College of Nursing called for a tougher approach to offenders by both police and hospital trusts.
Chief executive Dr Peter Carter said: "Something needs to be done about this major, national problem."
And senior NHS officials said many assaults were still not being reported.