Letters have gone out to 1,451 Police Community Support Officers, civilian investigators and call centre staff in the wake of a similar offer to more than 700 back office staff.
The force has not said how many workers will have to go, but Chief Constable Tim Hollis insists it will be a "modest" number.
He said the move would avoid having to take "draconian" action further down the line.
Assistant Chief Constable Stuart Donald said: "We have offered the opportunity for voluntary redundancy to all non- police officer staff.
"Clearly this does not mean that all of these staff members will be leaving us but it is sensible that we manage the business this way during what are undoubtedly challenging and uncertain times.
"We are also looking at our current business model to establish any areas which are suitable for appropriate staff members to be moved into, in order for us to maintain operational effectiveness across the area taking into account the potential loss of 30m from our budget."