Rawdata,
EASA/FAA (or Transport Canada) TPs do also test fly any new aircraft type prior to certification but usually the company TPs have already carried out the particular test point (designated as a "C" or Certification point and an "A" or Agency point in our company test schedules at least). FAA will also put a pilot through the proposed type rating training & verify, say, that a common rating with a previous version is possible. Rarely a pilot from a customer airline will also be invited into the evaluation pool but this is more likely to be during the operational test phase rather than the certification phase.
The Canadian DND, for one, will also test a civilian aircraft & do its own certification - for example the Canadair Challenger was test flown by a pilot from Cold Lake before it was given the CC-144 (CL600) and CC-144A (CL601A) codes.