The incident took place Wednesday night.
According to police reports, Sasco (given name Jeffery Campbell) was part of the shoot which featured American rapper J. Cole.
On leaving the set, the dancehall artiste discovered the passenger window of his Audi Q5 was broken and the document missing.
The matter was reported to the Admiral Town Police on Thursday, who are conducting investigations.
No arrest has been made.
Sasco has been creating waves internationally in recent times. His collaboration on Blacker the Berry with American rapper Kendrick Lamar went gold in April. The single sold more than 500,000 copies, making Sasco the first Jamaica artiste in three years to be on a single to achieve that status.
The Black Roses Corner was once a hot spot for flamboyant dancehall figures. Most prominent was choreographer Gerald ‘Bogle’ Levy who was killed in 2005.
Bogle was a key figure in the Willie Haggart-led Black Roses Crew. He created several dance moves including World Dance, Wacky Dip, and the Bogle.