What part of speech is overdress?

Overdress can be categorized as a verb.

Parts of speech

1. overdress is a verb, present, 1st person singular of overdress (infinitive).
2. overdress is a verb (infinitive).

Verb
overdress - put on special clothes to appear particularly appealing and attractive; "She never dresses up, even when she goes to the opera"; "The young girls were all fancied up for the party"
overdress - dress too warmly; "You should not overclothe the child--she will be too hot"