The way the head of state is chosen doesn’t really matter with regards to whether the state is a republic or a monarchy. Monarchies have crowned head of states,

The way the head of state is chosen doesn’t really matter with regards to whether the state is a republic or a monarchy. Monarchies have crowned head of states, republics don’t. For example, the Holy Roman Empire (aka this bundle of German states existing in the middle ages) was a monarchy, but the emperor was elected (by a set of dukes and such), whereas the UK is a monarchy while the queen isn’t elected.