Generally, official certification is not necessary unless it’s listed as a requirement or advantage for a specific government contract. Even without a certification, a business may be woman-owned, minority-owned, veteran-owned, etc. based on demographics alone for the purposes of nongovernment contracting or grants.
There’s not a broad certification process: a qualifying business must identify the specific government agency (federal or state) through which it needs to be certified in order to proceed with a particular contract or bid with that agency. A very limited number of local governments, like the City of Denver, will also sometimes require or request certification. There is no general or statewide certification issued by any agency that is applicable everywhere.
For the most part, a business doesn’t need to be certified by any agency to apply for grants, loans, education, etc. that are targeted to minority businesses. An organization would simply self-select its demographic information within the application paperwork. It’s the same for partnering with nonprofits or most local governments – unless the entity requires a specific certification, the business is already eligible and would mention that in an application, bid, or other communication.