The Doctor Takes a Wife (1940)

Stuck without a ride back to New York, and after some friction between the two, a best-selling women's author (Loretta Young) pushes herself on a doctor (Ray Milland) making the same trip.

A pit-stop along the way and the fact that after more sparks she stubbornly refuses to reimburse him for half the expenses (he then drinks the owed equivalent in cheap booze and crashes in her bed) result in the misunderstanding that they are married.

This is initially a tragedy for her because her bestselling book is aimed at single women; but then her publisher/wannabe boyfriend (Reginald Gardiner) sees potential gold in a different market in a second book in which she recants.

On his end, the medical school instructor obtains a much-desired promotion because of the (false) news of his marriage.

Seeing how, despite the fact that his fiancé (Gail Patrick) is not too happy about it, the situation still benefits both and they decide to play the married couple for a few months till they can safely get a divorce.

Being mostly familiar with Ray Milland from his dramas and even Horror movies I had never realized Milland started his career in comedies.

Milland is a surprisingly good straight man.
While he doesn't bring Cary Grant-levels of nuttiness and physical comedy required to make this a full-fledged Screwball Comedy (all the necessary ingredients are there: confused identities; crazy mix-ups; the war between the sexes; overcomplicated situations; running around pant-less; two different, simultaneous singing telegrams, etc.) he is certainly good looking enough to make a proper, comedic leading man.

Genre favorites Ray Milland, Edmund Gwen, and Edward van Sloan (also somewhere in there, is Abbott and Costello's Mike the Cop) are together in a film with no supernatural content whatsoever. ...Except that at the very end, a medical mannequin head inexplicably winks at the audience.

This is a favorite personal trope: non-genre movies which feature a single, subtle supernatural nod.