Our PhD students are required to pass an exam before they can TA - at least the foreign ones - ones from non-English speaking countries. However I am not aware of any such exam for new faculty.
With faculty, here, the chair of the department is required to certify to HR that their use of written and spoken English is adequate. I happen to know this only because I was acting chair for a month one summer when the department chair was away and I had to trek down to HR to sign the certification form for someone who still had a UK passport although a US doctorate and had lived in the US for 20 years. I don't know if the policy on faculty had changed some ten years later when I was director of graduate studies, and was able to get the requirement that non-US TAs take an oral test of their communication in English waived for an incoming grad student from Canada (though I knew, if the appropriate office didn't, that the student's first language was French though she had attended an English-language Canadian university).
Yes, in my state also the department chair has to certify that we are able to communicate effectively in English--both in written and spoken form. At my old institution there was no such requirement, and there were a few faculty in STEM fields who were just notorious for being incomprehensible--especially for undergrads. The biggest problem was when these folks would suddenly get assigned to teach a lower-division course that involved introducing masses of novel concepts and terms. The advanced undergrads and grad students had an easier time because they weren't trying to sort out new and unfamiliar vocabulary from the complexities of a foreign accent.
