I was pretty sure this had come up here before, but can't find any trace of it. It appears to be the Swiss equivalent of "maître d'oeuvre", i.e. someone who is in charge of all the "corps d'état".

Des soumissions sont alors envoyées aux maître d'états (entrepreneurs), qui ont un délai de 15 jours pour renvoyer une offre. ...
www.ecovie.info/index.php?to=2&so=2

1984 « Nouvelles notions de droit du maître d’état », cours destiné aux candidats à la maîtrise fédérale d’entrepreneur avec mise à jour complète en 1995 ...
www.cobaty.ch/Documents/CV_VD/cv_bettems_d.doc

le maître d’état (l’entrepreneur ou l’artisan) ;. -. le maître d’œuvre (celui ..... d’entreprise lorsque les défauts de l’ouvrage sont occasionnés par une ...
www.ffe-fbv.ch/fichiers-ffe/defauts dans la construction.PD...

Sous-traitant (entrepreneur, artisan, maître d’état) Mandataire (architecte, entreprise générale/totale, planificateur) Fournisseur (fabricant, distributeur ...
https://olmero.ch/fr/index.php?option=com_staticxt&staticfil...

You say that "the maître d’état is a person of responsibility on a construction site (along with the maître d’ouvrage)": note that the maître d(e l')ouvrage does not have a functional responsibility on site. He is the Owner of the the project, the Employer, and appoints the maître d'oeuvre (or in this case the maître d'état, presumably) to oversee the work on his behalf.

That is basically the rule. There are many variants, depending on the actual contract involved.


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Note added at 4 hrs (2008-06-03 22:18:23 GMT)
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Thanks to Matthew for finding the previous reference I couldn't find.

Consulting the glossary referred to there (put up by an architect), I observe that the equivalent of a "Maître d'Oeuvre" seems to be lacking, unless it is the "maître d'état".

Note that if we take "maître d'état" to be the equivalent of the French "entreprise", then it COULD be both the individual (sub)contractors doing diverse aspects of the work (painter, electrician, plumber) AND the Entreprise (with a capital E) in charge of the whole shebang (main contractor or prime contractor). The fact that the previous reference here was "maîtres d'état soustraitants" just might imply that you could have a "maître d'état" in charge of the whole show (the one who subcontracts work to the subsidiary "maîtres d'état").

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Note added at 4 hrs (2008-06-03 22:21:41 GMT)
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Sorry, the glossary I referred to is actually at another address:
www.letriangle.ch/fr/info/info_glossaire1.html


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Note added at 4 hrs (2008-06-03 22:34:15 GMT)
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The following suggests that the "maître d'état" is or at least can be the "maitre d'oeuvre" = main contractor:

Le devis des travaux ventilé par postes : il est établi par le maître d’état et l’architecte. Cet élément reste encore indicatif à ce stade préliminaire, mais permet néanmoins de définir une enveloppe financière globale. Il sera affiné par la suite sur la base des réponses aux offres de soumission ;
􀂃 Une liste des artisans ;
http://www.cvi.ch/fileadmin/user_upload/cvi/intranet/Article...

This is at the stage of issuing tender documents, IOW the contractors have not yet even put in their bids! Yet we have the "maître d'état" working hand in hand with the architect. This is what the "maître d'oeuvre" would do in France: the architect will be in charge of the "aesthetics" and some structural aspects (though there will also be a structural engineer, assuming that is not what the "maître d'oeuvre" is) while the "maître d'oeuvre" will manage the subcontractors, may well carry out some of the work (generally major structural aspects) himself, and report back to the Owner.