Essentially, the coop needs to incorporate, so you need letters and articles of incorporation, you need a charter and rules, an established board of members and registration with the province (and CMHC is a good idea).

CMHC is a great resource for this and they have a guide on the topic. https://www.cmhc-schl.gc.ca/professionals/industry-innovation-and-leadership/industry-expertise/affordable-housing/co-operative-housing-guide

I lived in and was on the board of a housing coop in Winnipeg, DM me if you want details or an introduction to speak to them.

Edit: provincial rules for starting a coop aren’t very strict in Manitoba, housing coops are particularly unobstructed in mb as well. https://www.gov.mb.ca/jec/busdev/coop/index.html