When is it appropriate to use a university seal as a graduate student, post-doc or research scientist? 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?
It is my personal understanding as a professor and former chair of a program that you can use the letterhead for job searches as long as you retain a position of some kind at the university: postdoc, doctoral candidate, visiting professor, lecturer, research scientist, etc.  

As an appropriate proxy, use the letterhead as long as you have a university e-mail address (that isn't an alumni one).

Once you're no longer affiliated with the university because you graduated or separated, then you should not use the letterhead.

[Note that use of letterhead for job searches is a special case. Do not use the letterhead for other personal purposes - such as writing a letter to your congressperson - if you're in a liminal position as the possible blowback can be hazardous to your career].