According to Turner's book The Thirty Days to Hitler, there were local council elections held in Saxony the week after the Nov 32 Reichstag elections, and then some more local elections in late November in Bremen, in addition the Lubeck and Thuringia local elections. In the case of Bremen I don't know what type of elections they were since the website that lists the lander elections during Weimar has Bremen elections, but doesn't show any 1932 results.
In all of these cases, the Nazi vote was falling from the November reichstag results, but I still haven't found the detailed breakdown, outside of the Lubeck results which are on the Weimar lander election results website.
Until 1937, Bremen state consisted of the cities of Bremen, Vegesack and Bremerhaven and a number of "rural" towns (all of which are now within the city of Bremen). So presumably there was a local layer of governance... although, just as in Hamburg, the city was already over 90% of the whole.
