A man was found dead at his sheltered accommodation in Sorrel Grove, Erdington.
A post mortem examination carried out on October 15 showed that Leonard Sandel, 67, died of a neck injury.
As part of the investigation, a 48-year-old woman and two men, aged 42 and 39, have been arrested on suspicion of murder.
They have been released on police bail pending further enquiries.
The CCTV image released shows Mr Sandel using a cash machine on Tyburn Road on October 3, at around 7.30pm.
Police are appealing to anyone who may have seen him to get in touch.
They need to understand his whereabouts as they believe he may have been killed that day.
Mr Sandel’s family have said that he will be sadly missed.
Detective Inspector Michelle Allen, from the homicide team, said: “Mr Sandel’s death is very sad. We’re working hard to determine exactly what happened to him.
“While the arrests are a significant development in our investigation, I still need to speak to anyone who may have seen Mr Sandel before he died, possibly on the Tyburn Road on 3rd October, or around his home in Sorrel Grove.
"I’m also asking anyone who was driving through this area on the evening of the 3 into 4 October to check their dashcams. Please contact my team as soon as possible if you have any information that may assist us."
Anyone with any information is urged to contact police via Live Chat on the West Midlands Police website, or call 101 quoting log number 2246 of October 7.