Trevor Browne High School in Phoenix az
I am the theatre teacher at Trevor Browne High School, and I am close to the theatre teacher who was here when the building was built. No one died when the building was built.
I have heard that a girl went missing around the time the theatre was built, and my students swear that they have seen her around the theatre.
Story: my students were performing a show and they saw a big black blob floating over the set, and they also saw a girl with black hair in the hallways. Turns out that the girl who went missing had black hair.
There is a ghost, but not a construction worker. :)