Officers were called to Mappin & Webb, in Coney Street, at around 4.40pm. on Tuesday, July 26, after multiple reports of a disturbance.
North Yorkshire Police said when they arrived a man was being restrained by a member of staff at the store and members of the public.
A spokesman said: “Unfortunately the man, who has been named as Samuel Diatta, aged 39 and from York, began to experience medical difficulties and was taken to York District Hospital where he was sadly pronounced dead shortly after 6.40pm.”
A medical investigation is being conducted into the cause of his death.
Three men who were arrested have been released on bail.
Mappin & Webb earlier described the man who died as a “client”, saying in a statement: “Our thoughts are with the client’s family at this time.”
The company sells luxury brands including Rolex, Cartier and Breitling watches costing thousands of pounds.
Senior investigating officer Det Insp Steve Menzies, of North Yorkshire Police’s Major Investigation Team, said: “This is a very tragic incident. The three men arrested in connection with the report have been interviewed and released on bail pending of the results of police and medical investigations.
“Samuel’s family are being supported by specially trained officers and I would ask that their privacy be respected to allow them time to grieve their loss.”
The force was referred to the Independent Office for Police Conduct due to officers’ involvement in the incident before Mr Diatta’s death.
Anyone who witnessed the incident should call 101 and ask for the Major Incident Squad.
If you prefer to remain anonymous, you can pass information on to Crimestoppers on 0800 555111.