Officers were called to reports of a white Vauxhall Corsa on a bollard in a car park for Sutton Park, accessed off Park Road in Sutton Coldfield, at around 12.50pm on Wednesday, September 9.
The driver, in his 60s, was treated by paramedics, but was pronounced dead at the scene.
A West Midlands Police spokesman said: "It is understood he may have suffered a medical episode and officers from our serious collision investigation unit are working to establish exactly what happened.
"We are appealing for anyone who saw the driver before he got into the Corsa or the car colliding with the bollard to get in touch."
Anyone with information is asked to call West Midlands Police on 101, quoting log number 1826 of September 9.