Catalysis of the reaction: cis-4,5-dihydroxycyclohexa-2,6-diene-1,2-dicarboxylate + NAD+ = 4,5-dihydroxyphthalate + H+ + NADH.
cis-4,5-dihydroxycyclohexa-1(6),2-diene-1,2-dicarboxylate:NAD+ oxidoreductase activity