Personally I'd say UK/USA

Screenshot from the end of the film showing more production companies.

Based on the sequence of production company names in the opening/end credits and copyright (see NOTES), I would list the companies and country of origin as follows:

STUDIOS
Columbia Pictures Industries
Eon Productions
Danjaq

COUNTRY OF ORIGIN
United Kingdom
United States
Czech Republic

Hope that helps.


NOTES:
[1] Film credits and copyright:
00:03:48 > ALBERT R. BROCCOLI'S EON PRODUCTIONS LTD. presents
02:23:38 > Casino Royale © 2006 Danjaq, LLC, United Artists Corporation and Columbia Pictures Industries, Inc.
02:24:21 > A UK - Czech - Ger - US Co-Production
                A STILLKING • CASINO ROYALE PRODUCTIONS LTD • CASINO ROYALE US LLC • BABELSBERG FILM CO-PRODUCTION
                Made by Eon Productions Ltd. and Casino Royale Productions Ltd.
02:24:27 > RELEASED BY COLUMBIA PICTURES


[2] Production companies in order of appearance:
• EON PRODUCTIONS LTD. ==> (UK): https://opencorporates.com/companies/gb/00697555
• DANJAQ, LLC ==> (USA): https://opencorporates.com/companies/us_ca/199701010026
• UNITED ARTISTS CORPORATION (USA)
• COLUMBIA PICTURES INDUSTRIES (USA)
• STILLKING FILMS ==> (Czech): https://filmcommission.cz/en/director/stillking-films/

• CASINO ROYALE PRODUCTIONS LTD ==> (UK): https://find-and-update.company-information.service.gov.uk/company/05507180
• CASINO ROYALE US LLC ==> (USA): https://opencorporates.com/companies/us_ca/200528710065
• BABELSBERG FILM GmbH ==> (Germany): https://opencorporates.com/companies/de/G1312_HRB8051

[3] Film copyright displayed full company name for release studio tradename "Columbia Pictures":
    https://uspto.report/TM/72441192 (rules state not to truncate the company name).

[4] Film's copyright registration (https://uspto.report/copyright/12124053) showed Danjaq, LLC, United Artists Corporation and Columbia Pictures Industries, Inc. were "employers for hire", that is, they were the authors of the film, which makes them production companies as well.

Quoting Wes Carpenter:

Quote:
Seriously guys? The end credits make a definite and first hand statement about the countries of origin (see the screenshot above), and you want to change that?

Isn't there a difference between a list of countries at the end of the credits and the specific rules about the order in which those countries should appear depending on the role of the studio?

Quoting ObiKen:

Quote:
My understanding is the rule for country of origin states to use the production companies in the order they appear in the credits.

Yet, in this case, they are clearly in the wrong order in the credits.

Quoting Lithurge:

Quote:
Quoting GreyHulk:

Quote:
Quoting ObiKen:

Quote:
My understanding is the rule for country of origin states to use the production companies in the order they appear in the credits.

Yet, in this case, they are clearly in the wrong order in the credits.

And hasn't it always been the case we follow the rules regardless?


Clearly the film makers thought this was the correct order, regardless of profiler rules or wikipedia.

This is my understanding:

The multilateral "Co-Production" credit in Casino Royale (2006) was a requirement of Article 12 in the "European Convention on Cinematographic Co-Production": https://www.wipo.int/wipolex/en/text/502395

Article 2 in the convention states a co-production must comprise of at least three (3) co-production companies from three signatory countries of the convention. In addition, a fourth party that is NOT a signatory country of the convention may be added, as long as their contribution is kept below 30% of the film's production cost.

So when I see the credit "A UK - Czech - Ger - US Co-Production", I see the three signatory countries of the convention listed first followed by the non-signatory country.

On the other hand, the listing of production company names in the film's opening/end credits was the sole responsibility of the producer(s), not the "European Convention on Cinematographic Co-Production".

Hope that explains the discrepancy.