Most states have a test about the relevant laws. Usually covers if a psychologist can admit someone to the hospital, when to call child protective services, when disclosures are permitted, don't have sex with patients, how much CE credits you need, etc. it's typically open book, and the questions are phrased verbatim out of the law. Control F can basically get you to a passing grade. This is why I typically recommend slamming ones head against a hard object as the appropriate method of preparation for this exam.
Some states have an oral exam. They tend to be very collegial and focus upon the basics of practice and the local laws. Pretty easy.
Louisiana has requirements to use the title neuropsychologist. You have to add in stuff in your application and the oral exam covers more stuff in this area.
Louisiana, New Mexico, Illinois, and Iowa require one to pass the PEP exam to practice as a prescribing/ medical psychologist. Illinois has some other requirements as well. Guam has basically no requirements for this. The DoD and IHS require state licensure as an MP.