We are ALL certified as officials for the OHSAA after taking the State Refereeing course, passing the test, and then enter as a Level 2 official. To be Playoff eligible, we must upgrade to a Level 1......which involves being Assessed on a number of games (passing those Assessments), passing another upgrade test.
Playoff Assignments are based upon points that that Official receives, which is a product of both the ratings that coaches & ADs give you for games you've officiated for them, multiplied against the points received from being selected to a Top 15 list, that every school is (theoretically) required to submit to the Main Office. Associations, Assignors, the District Boards, and others also turn in those lists. That final point total then places us in one of three Pools for the Post Season: State, Regional, & District. Obviously anyone in a State Pool can work games at all 3 levels. the State & Regional Pools are 3x larger than the total number of slots available, so Pool placement doesn't guarantee a game assignment.
State & Regional Assignments come from Columbus. Multiple factors enter in.....age, experience, travel distance, etc. are all 'possible' factors; you'd have to ask them for more specifics. Generally, an Official will receive only 1 State Game per post season, IF they get on. Regionals used to be multiple, but they too have for the most part are now 1 only per Playoff. I had 2 Regionals in '09,'10, & '11......and like many other officials, 1 only in each year since.
District assignments used to be made by one singular District Assignor; this year it seems it was a collective effort by each of the various District Athletic Boards.
There are also seasonal requirements we must meet to remain Playoff Eligible......minimum number of local meetings, minimum number of games officiated, etc.
I hope this helps. This is just 'scratching the surface', an over view, only from my perspective. It's more involved than this I'm sure.