May I use my graduate school's letterhead right after graduating, when applying to jobs? I just completed my MFA in Film this August, 2017. Now I am freelancing and not associated with an academic institution. May I still use my graduate university's letterhead when applying to faculty positions? I don't have any other nice looking letterhead with a logo, unless I make it up.
No you may not. The use of an official letterhead implies not only a current affiliation with the university, but it some countries and contexts also implies that the correspondence is for official purposes. Each university has it's own rules and policies, but I would be shocked if your university would consider this acceptable, and both universities that I have attended have specific guidance to not do this. In general, you do not have the right to use that letterhead simply because you attended the university, and using it in that fashion is inappropriate because you are representing yourself as having a professional position that you don't have.