For this kobietę is in accusative. But in another problem "I touched the animal" was translation to "Dotknąłem zwierzęcia" where zwierzę was in genitive. Is there something I missed or is this a mistake?
Yeah this is some very complicated stuff even for natives. Even in the sentence you quote, the accepted version was in Accusative until someone recently pointed out that according to dictionaries, it should be Genitive.
So this is what the rules say: in a literal, physical meaning, 'dotknąć' takes Genitive. In a metaphorical, psychological(?) sense, it takes Accusative. So "Mężczyzna dotknął kobietę", whether it was done on purpose or not, means that the woman was hurt by something the man did or didn't do or said or didn't say.
I believe a lot of educated natives don't even know about this differentiation, though.