The project is estimated to cost the trust about GHC3.2 million.
Alhassan paid a courtesy call on him at the SSNIT Head Office in Accra.
He said each of the projects would have a charge office, a cell, a washroom (W/C/bathroom) and a terrace.
He said the initiative was part of the Trust's social protection policy, which was expected to see an increase in police visibility country-wide.
The move by SSNIT is also expected to see an increase in police presence in the country.
The Ghana Police Service has 11 police regions (including Tema), made up of 79 divisional headquarters, 275 district offices and 1,000 stations and posts.
Only 7,248 officers are properly accommodated, while 14,000 are not so properly accommodated.
The unknown residences are estimated at 9,000, while rented accommodation stands at 424.
Mr Alhassan expressed gratitude to the management of SSNIT for its decision and pledged to ensure that the stations were spread strategically to check crime in the country.