The statement said police had been in contact with Martin’s family since the incident.
“The family has requested privacy as they grieve this tragic loss,” it read.
“No additional details are being released at this time, as this remains an ongoing investigation.”
The officers involved in the incident have been placed on paid administrative leave, in accordance with Oakland Police Department policy.
Martin spent six of his seven NFL seasons with Tampa Bay after starring at Boise State University.
Diminutive by NFL standards at just 1.75m, he was known for his physical play.
Martin piled up 5356 yards and 30 touchdowns in his NFL career, his best season a 1402-yard campaign in 2015 that included six touchdowns, an additional 271 passing reception yards and a TD catch.
He finished his NFL career with the then-Oakland Raiders in 2018.