Since you've already accepted "precinct" (see KudoZ http://www.proz.com/kudoz/354721) as the translation of "brigade," it only stands to reason that what is being commanded is a precinct!

Note that I get 1,040 hits on Google for "precinct commander"! See:

--------------------------------------------------
Note added at 2003-02-10 18:44:07 (GMT) Post-grading
--------------------------------------------------

This can either be a *police squad* (large police force) or a *police station* (small town) - I suspect you\'re dealing with a commander of a police *squad*:

From the Oxford SuperLex (Oxford 3-in-1) - note the second definition, and \"brigade de gendarmerie\":

brigade / b1igad / nom féminin
1 armée brigade; brigade aérienne airborne brigade; brigade
d\'infanterie infantry unit;
2 (dans la police) squad;
3 administration (groupe de travailleurs) team.

brigade antiterroriste antiterrorist squad;
brigade criminelle crime squad;
brigade financière fraud squad;
brigade de gendarmerie (gendarmes) (small town) police
force; (bâtiment) small town police station;
brigade des mineurs juvenile delinquency division;
brigade des mœurs or mondaine vice squad;
brigade de sapeurs-pompiers fire brigade GB, fire
department US;
brigade des stupéfiants drugs squad GB, drug squad US;
Brigades internationales histoire International Brigade (sg);
Brigades rouges histoire Red Brigades.