The Habitat Co., a property management firm that oversees about 3,400 units of public housing for the Chicago Housing Authority, has moved to end its management agreements with the agency after almost 40 years of partnership. Correspondence obtained by the Tribune Friday reveals that on Sept. 6, the Habitat Co.’s president, Matthew Fiascone, informed CHA that his firm was denying the authority’s request to extend the company’s property management contracts for the next year.