I am applying for tenure-track positions at other universities after having recently completed my PhD. I am still technically a graduate student until my degree is conferred in a few months, and I am employed and acting as a post-doc in the meantime.
After wondering if it is acceptable to use my current school's seal on the letterhead for my research statement, statement of interest, and the like, I decided to look up general guidelines for when to use the seal, and I couldn't find much.
Another answer mentions it is unacceptable to use a school's letterhead for something totally unrelated to the university, but it does not answer the general case for when a graduate student (and above ranks) should use the seal. In my special case, I think me going on to become a tenure-track professor in the same field is very much in the interest of my advisor and our school.
With that background in place, I think the general question is the better one to ask here: When is it appropriate to use a university seal on a letterhead?