Not sure what the German constitution said back then, I suppose a coalition government was required if all parties failed to get a majority.
That's the problem, it wasn't and that's one of the reasons the Weimar Republic failed. The people elected the Reichstag but the Chancellor was appointed by the president. In theory the president would appoint a chancellor who was supported by a majority of the Reichtag, in reality that didn't work at all and Germany had a revolving door of chancellors. Government after government failed because the chancellors were unable to get a stable coalition to work in the parliament.
Hitler never had a majority, not with the people or within the Reichtag, during the first year of his reign he was scared shitless of Hindenburg (the president) because he could have kicked him out of office any time he wanted. It was only after Hindenburg's death that Hitler was able to merge the offices of chancellor and president and really take over.
The constitution was pretty fucked up and it was a deliberate decision for today's germany to have the chancellor elected by the parliament (not by the people!) to ensure a government backed by a majority. The members of the parliament can simply elect a new one anytime they want