The incidents took place on the A44 Bromyard Road on Friday afternoon (July 14).
“Officers responded to a single car collision at around 4pm on Friday,” a West Mercia Police spokesperson said.
“As officers were making the scene safe, a vehicle made contact with the parked police car.
“No arrests have been made and no injuries [were] sustained.”
Police had to close off one lane of the road for a couple of hours during the Friday rush hour, causing long queues of traffic on the A44.
The crash itself happened at Broadwas, eight miles east of Bromyard.