The dead had originally been brought to the jail's detox facility.
Aamulehti reported on Sunday that a man brought to jail on May Day eve had been found dead.
The case is being handled by the Western Finland Prosecutor's Office. District prosecutor and the lead investigator on the case, Paula Pajula, told Aamulehti that the intoxicated man had not gotten along with the staff.
According to Pajula, a doctor examined the man before he was transferred to police custody.
The case has also been reported by national broadcaster Yle and Finnish language evening tabloid Iltalehti.