If it's a co-production, it would technically be the "U.S. Premiere" at the second theater. La Jolla and Papermill would share that distinction because they're exclusively co-producing the premiere. Where it plays when is somewhat irrelevant, as it's the same production just moving to a new theater (and THAT particular production is a "U.S. Premiere" production).
ETA: Just to clarify further, it doesn't matter which theatre company gets it first or second. They both have a hand in mounting the "U.S. Premiere" as co-producers and presenters. So yes, they can both receive the credit of premiering it. If La Jolla had exclusively premiered their own production and did it before Paper Mill's, they could be the only company to claim ownership of that distinction, but this is joint production where the same cast & crew are traveling with the show to both coasts. They're also sharing in the production costs, so it's a no brainer.
Updated On: 2/26/14 at 04:21 PM