Police are calling for sightings of 68-year-old Tametame Wiremu around Auckland city this month.
The Manurewa man, also known as Tommy, died after being admitted to Auckland Hospital on May 12.
Police are tracing his movements between 9am and 1pm on the same day.
They would like to hear from anyone who may have seen him on Victoria St, Lorne St, High St or Queen St during those times.
He was of solid build with a shaved head and long white beard and wearing grey trackpants with two white stripes down the leg, a black polo shirt, a grey jersey with black panels down the sides and grey or black slippers, police said.
CCTV footage shows Mr Wiremu removing his jersey at some point during the afternoon, police said.
Police were also searching for a manila folder containing documentation that Mr Wiremu was carrying.
Any information can be provided to Operation Oregano on (09) 302 6406 or anonymously through the Crimestoppers line on 0800 555 111.