Completed in November 1973, according to Offbeat:
New May House was built from 1971 to 1973 to replace the then May House in Gloucester Road which was more famous for its curries than as a police building. The new May House became fully operational in November 1973 after a plaque-unveiling and opening ceremony, at which Princess Alexandra and then Commissioner of Police Charles Sutcliffe officiated.
At the time, May House was considered to be a model of efficiency. Costing some $24 million, the 20-storey building mainly housed Headquarters Crime units, Communications and Transport, Personnel and Administration. It also had a lecture theatre, an officers' mess, a canteen and an indoor firing range which was modelled on the Federal Bureau of Investigation Headquarters firing range in the United States.
It was demolished in 2000, according to Legco:
The demolition of May House is scheduled to commence in January 2000. We plan to complete all stage 1 works around June 2000.