Well I'm talking about who owns the property, not the distribution rights.
CBS, but there are things in Star Trek movies that use trademarks established in the TV series so Paramount has a contract with CBS to get those rights. What we don't know for 100 percent is if the rights are doing the films in general, or just rights to certain trademarks of things used in the film (and thus merchandising). For the purpose this topic, TV series are all up to CBS .
But wouldn't his packaging say...
My Bluray for STID says © 2013 PARAMOUNT PICTURES ALL RIGHTS RESERVED STAR TREK and related marks and logos are trademarks of CBS Studios Inc. and Paramount Pictures.
...if Paramount owned any part of the franchise?
The thing that still seems to make the most sense is that CBS owns the intellectual property and Paramount licenses it from them.