I don't know if "Services reserved to the staff" is correct, or if I should write "STAFF RESERVED SERVICES" or something different :)
Based on your question's title, I'll take services to mean service areas such as the kitchen, pantry, etc. My reading of your question is that you want to know what to call places that only staff are allowed into.
The term reserved to has the notion of benefits that are kept or allocated to someone. The meaning of the term is loosely based on the meaning of reserve:
reserve verb 2 Kept specially for a particular person. ‘a reserved seat’ - ODO
However, typing "reserved to the" into Ngram and clicking through to the textual instances demonstrates that the force of the phrase isn't so much on the keeping part, but instead that it's kept for someone.
In your example, although calling services areas places that are reserved to the staff is comprehensible to native speakers, it elevates the status of those areas to something of a privilege. But this might not be the way the staff think about those areas since they are places of hard work.
Note that you can use the word restricted instead of reserved.
restrict verb 1.3 restrict something to Limit something to (a particular place, time, or group) ‘the Zoological Gardens were at first restricted to members and their guests’ - ODO
The intention would be to say that only staff can access the area. Unfortunately, restricted can also be used as an adjective, giving the opposite meaning:
restricted adjective 1 Limited in extent, number, scope, or action. ‘Western scientists had only restricted access to the site’ - ODO
So if you say that the area is restricted to staff, it could mean that only staff can go there, or that staff aren't allowed to go there. This is hardly satisfactory.
In practice, you can get around this by labeling the area itself as a restricted area (here is a link to some signs along these lines):
An area that only authorized people can enter. - wikipedia
You can also just say Staff Only.
Here's an example that uses both ideas:
As TeacherKSHuang commented the most professional way to say this it to use set phrases:
Reserved services (For staff only) - "For" is optional here. You can (if you want) capitalize it like this "Staff Only"
Staff-only reserved services
If you still wish to use your example then it should be:
- Services reserved for staff only