The history of a house can be researched in city offices such as an historical preservation office, assessor's real estate office or office of the city clerk or at the public library. The research into a house's history will typically involve more than one office, and can include an historical society or the National Register, depending where the research leads.
One good place for a researcher to start is to determine whether the house is in an historic district. If it is, there is the possibility that someone has already done the research. The city assessor's office can help determine the date the house was built. This allows researchers to find permits, deeds, maps and directory listings pertaining to the house.