Police are investigating the cause of the accidents just after 7pm on March 13.
A police BMW, Yateley's new area car, was travelling towards Hartley Wintney, between the Hawley roundabout and The Ely pub, when a deer ran into the road.
Pc Jamie O'Brien swerved to avoid it and the BMW veered across the A30, hit two trees and spun back on to the road. His colleague Pc Andrew Cockayne broke a wrist.
Meanwhile a Vauxhall Corsa carrying three soldiers from Gibraltar Barracks in Minley swerved to avoid the police car, hit some trees and rolled to the bottom of the embankment.
Yateley firefighters released the soldiers by removing the Corsa's windscreen and they were taken to Frimley Park Hospital.
Two were released later that night but the third was detained with concussion.
The road was closed for five hours as the crash investigation unit examined the scene.
Sgt Barry Taylor of Farnborough traffic department said: "I would hope to conclude the inquiry within weeks.
"The crash investigation unit and photographer were called to the scene and both cars will be examined to find out if either had any faults that may have contributed to the accident.
"Both drivers have independently stated there was a deer in the middle of the carriageway and there were other witnesses who I will be contacting.
"However, if there are any witnesses who haven't already come forward I would be pleased to speak to them."
Call Sgt Taylor on 0845 0454545.
Our picture shows the wrecked BMW.