According to detectives, the maintenance manager was doing his normal rounds around 6:30 a.m. when he found a man who appeared to have been shot once in the head. The man was lying on the top floor of the garage at 1400 Binz St.
He was fully clothed, and so far no weapon has been found.
Authorities believe he is in his 30s.
Police say it's unclear if he's homeless.
The museum was not open at the time and has been closed due to the COVID-19 pandemic.
If you have any information about this shooting death, you're urged to call HPD's Homicide Division at 713 308-3600 or Crime Stoppers at 713-222-TIPS.