The Police Investigations and Review Commissioner has been asked by prosecutors to look into the circumstances leading up to the death of Steven Chesney.
Mr Chesney died at Wishaw General Hospital after becoming unwell on arrival at Motherwell police station.
The watchdog will report its findings to the Crown Office.
Assistant Chief Constable Malcolm Graham said: "Our thoughts are with the family at this tragic time.
"We can confirm that the Crown Office and Procurator Fiscal Service (COPFS) has instructed the Police Investigations & Review Commissioner (PIRC) to carry out an independent investigation into the circumstances leading up to the death of a 33 year old man at Wishaw General Hospital who became unwell on arrival in police custody within Motherwell Police office on Sunday 1st May 2016."
Scotland's police watchdog has begun an investigation after a 33-year-old man died in police custody at the weekend.