Regarding brown trout in North America see:

MacCrimmon, H. R., and T. L. Marshall.  1968.  World distribution of
brown trout, Salmo trutta.  Journal of the Fisheries Research Board of
Canada 25:2527-2548.

It's a bit dated, but things haven't changed much since.  Established
populations exist in at least 34 U.S. states and most Canadian provinces.

Al Zale