I would recommend doing crisis intervention without police involvement. Someone in a mental health crisis doesn't need police, sirens, lights, someone with a gun, handcuffs, etc.
Eugene, Oregon has the CAHOOTS program that has been in operation for 30 years. They are funded through local law enforcement in Eugene and Lane County. They do not go out with police (thankfully), but have called police in extreme situations. They have had over 240,000 calls and only asked for police backup in 250 of them.
Additionally, Denver has a similar program (not sure of the name), and here in Sacramento, there is a newer program that is volunteer only at this point (we are trying to get the County and/or the city to fund the program so it can operate 24/7), called Mental Health (MH) First. https://www.antipoliceterrorproject.org/mh-first-sac
Mental health should not be criminalized or resolved with incarceration. Additionally, this often includes unhoused folks who simply need housing to be able to start addressing other issues adequately.