Hi NatureBucket,
Personally I find more scope to this if the psychiatrist is the protag -- it lends itself to a more compelling ride if we are forced to question whether or not this guy is telling the truth or not... we'd get that from the psychiatrist's POV -- just imo...
Also, the purpose of a logline should be to describe, as succinctly as possible, the main ACTION of the film... as dpg mentioned, what you need to focus on is what your protag actually does as a result of a decision --this prompts action, which is what readers want to see in a logline, and what paying audiences want to see in a cinema.
I can't see any real stakes here atm either, as, if the Dr has no pre-existing belief in extraterrestrials, or any valid proof from the patient (or any emotional influence, like the 'L' word...) then I can't really see a dilemma -- She's 'rigid and rational', and would simply be doing her job (duty) by committing him. If any of these elements existed in the logline (i.e. she begins to investigate his claims of the abduction and comes across some clues that convince her he may well be telling the truth/ she falls in love with him/ has witnessed some kind of unexplained alien type sighting in her own past etc etc etc...) then I think the logine/ story would have potential.
My examples below are probably not what you have in mind story-wise, but just to show a potential couple of angles etc...
'After falling for her seemingly delusional patient, an ?ber rational psychiatrist helps to break him out of a high security hospital in order to rendezvous with aliens that he claims had previously abducted him.'
or
(obviously a tad long...) 'After discovering her violent patient is telling the truth about his family being abducted by aliens, a highly strung psychiatrist breaks him out of a high security hospital in order to rendezvous with the aliens before he is committed for life.'
Anyway -- best of luck -- does have potential and has hints of Terminator 2/ Close Encounters/ and even Bram Stokers Dracula (well -- the stuff that deals with the mental patient etc...;))