It is not the Distributor, as we don't track local theatrical distributors. A 'Theatrical Release Studio' aims specifically at the large, vertically integrated US media corporations (aka "Majors"), that finance (or buy) a movie, and distribute those movies themselves (or sell distribution rights). They can also be the actual production company (in business terms a total vertical integration), but they don't have to. Ususally those companies/business units are credited as "XY presents" – at least in US productions and films sold to local markets by US companies. Only those companies we track, and we list them first.

To give a few examples: Warner Bros. Pictures, Twentieth Century Fox, Universal Pictures, Paramount Pictures, Columbia Pictures and Touchstone Pictures/Walt Disney Pictures are the six most common 'Theatrical Release Studios' – they finance the movies (before, during or after the production), they usually self-produce or at least co-produce the movies, and they usually distribute those movies worldwide themselves, through distribution partners (no credit), or through sale of the distribution rights (no credit).

The second group of companies that fall under the term 'Theatrical Release Studio' are "mini-majors" like Lionsgate/Lions Gate Films, The Weinstein Company (with sublabel Dimension Films), DreamWorks Pictures, Metro-Goldwyn-Mayer Pictures, Summit Entertainment, Lakeshore Entertainment, Focus Features (with sublabel Rogue Pictures), Miramax Films (former Disney subsidiary), Regency Entertainment, and subsidiaries of the six Majors, like Screen Gems & TriStar Pictures (Sony subsidiaries), New Line Cinema & Castle Rock Entertainment (Warner subsidiaries), Fox Searchlight Pictures (TCF subsidiary) and so on. Those companies usually either finance/produce a movie themselves or aquire worldwide or multi-territory distribution rights to a movie. Those businesses have usually only US distribution units, so they frequently sell distribution rights for a limited time to local distributors (or use their parent companies' distribution units) but retain copyright and full credit.

In basically all those cases the 'Theatrical Release Studio' will be the company (or companies), that is listed in the written opening credits as "XY presents". And also keep in mind that in many cases you won't find suitable 'Theatrical Release Studio', as vertically integrated media corporations are rather seldom outside the USA. An European or Asian production won't have a 'Theatrical Release Studio' as production and distribution usually are separate – in this case simply move on to the credited production companies.

Quoting TheMadMartian:

Quote:

The Theatrical Release Studio is the company responsible for distributing the films to the various movie theaters.  It may, or may not, also be the production company.  Unfortunately, some research will be required to determine whether or not they are.

This is only correct for the US system, and even there only to a certain point. In Europe most Paramount & Universal productions were distributed through United International Pictures (UIP), but we don't credit that company ever. We also don't credit Kinowelt, or Concorde, or Senator for films they distributed for New Line, Miramax or the Weinsteins in Germany. The 'Theatrical Release Studio' is a very US-centric concept to name companies that control distribution, but they don't even need to distribute their films themselves.

Quote:
As an example, Disney produces and releases their own films.  They also release films for DreamWorks...who produce but do not release their own films.

Not anymore, but even when DreamWorks used to distribute their film themselves in the US (through 'DreamWorks Distribution', which never was credited), their films were distributed by UIP outside the US. And we still always consider DreamWorks to be the TRS in all those cases, because Dreamworks was in control of distribution and retained its credit ("DreamWorks Pictures presents") – that's the credit we always tracked.

The 'Theatrical Release Studio' is simply not the (local) film distribution company. The term is meant to fit 'United Artists' under it, as they were considered a "Studio", even they rather seldomly produced films themselves. 'Lions Gate Films' is a similar construct, they mostly buy films to sell distribution rights worldwide, handling only US-distribution themselves. But they still get the TRS credit on basically every Non-US release I've seen, even they don't distribute films theatrically outside the US and Canada (Maple).

Most productions outside the US are independent productions, those are handled completely different. A production company will most likely approach a local distributor for domestic theatrical distribution and an also independent film sales company, that will try to sell non-domestic distribution rights to other local distributors (or a larger film sales company). What's in this case the "Theatrical Release Studio"? 
You either won't have a TRS (which is perfectly fine, because most parts of the world don't use the US distribution system), or you'll end up with all film sales companies, that have actually paid the producers an upfront fee to get their own credit in the film (like actually some of the US mini-majors do...).