References check for a tenure position? I understand most parts of the hiring process for an academic job, except for the reference check. How do they check it, who checks it, and when do they check it? Do they check what we write in the cover letter, cv, teaching/research statement, etc.? Do they run a background check, credit score check on you?
At my institution in the United States, reference checks are done by members of the search committee for the position, who call those people the candidate has listed as references.  We use a structured list of questions, ending with, "is there anything we should know that I haven't asked you?"

We verify academic credentials by requiring official transcripts, including those from undergraduate institutions.

The institution separately does a criminal record background check, handled by the university police department.  The candidate must explicitly authorize this, in writing.  But, of course, we cannot consider candidates who will not agree to the background check.  As far as I know, there is no credit check for faculty jobs.  There probably is a credit check for anyone who handles money.

Finally, the institution does a driving record check every year.  This is because we are covered by the university's insurance when driving university vehicles or driving our personal vehicles on university business.

What I've written (except the bit about the driving record) applies to people being hired into a tenure-track position.  Applications for promotion or tenure for those already on the faculty are much different.