Design Engineering Approval
First, let's define what engineering approval we're talking about. Is this design engineering, process engineering?
Design Engineering: An engineering approval is done any time there is a design approval or when there is a change where engineering is involved. For example, if I have a foundation brake assembly and find that a certain spring does not meet spec and I talk to the manufacturer and it turns out I screwed up earlier and should have had looser specs on the spring tension at a given length. Or - maybe a spring which is seeing field failures and a design change recommendation (request, whatever). Someone submits the 'recommended' change to design engineering because they own the print which calls out the spring characteristics. I may want and need the change but I can't have it until I have design engineering approval which involves a print revision. Often the engineering approval, as Al pointed out, is not a stand alone document but rather is a place for a signature on a larger form - such as an engineering change approval form where multiple groups have to sign off.
The engineering approval would be part of the PSW package if you have to go back through that (often for a change you can get approval to do a subset rather than go through the entire PPAP process - it depends on how extensive the change is, it's impact, etc.). Of course, this is assuming the part is already in production. In most of these situations there are typically a number of 'functional groups' (such as the process folks) who may also have to approve the change.
So - you may need a engineering signoff several times in the life of the part after the initial release - not just at the release (start of new part). Your design change system should define how it works where you are.
Or - maybe I'm lost on what's being asked. I'm somewhat confused today. Too many balls in the air.