Should new plywood be installed over old separating plywood?
If the old plywood was clean and not infested with dry rot or mold it should be OK to cover it with the new plywood. One thing to consider is that the new plywood probably wants to be the same thickness as what would be used if it was used by itself on the rafters (i.e. if the old plywood had been removed). This will ensure that the strength of the plywood is enough to bridge spots on the roof where the old plywood was weakened to the point that it would sag under the load on the roof.

You also should consider the design parameters of the roof to ensure that the extra weight of the added plywood is well within the static load capability of the roof support structure. 

Lastly it would be best if the new sheets of plywood were offset from the seams of the existing plywood but at the same time placed so that the new seams can be properly nailed into the rafters and other roof structure members. It is unlikely that seams of new plywood simply nailed at random locations into the relatively thin old plywood will be assured to keep the plywood held down over time.