It depends!
Sometimes governments aren’t really involved in co-op business. In other cases, government does play a significant factor.
This can be the case where a co-op:
In any of these situations, government may set rules about who can live in the co-op buildings, or what housing charges should be, or what kind of reports the co-op should submit.
All housing co-ops have to follow laws that apply generally, such as human rights and privacy legislation.