The city of Hartford, upon approval of its legislative body, may negotiate and fix assessments on improvements for retail, commercial and housing purposes during the period of construction of such improvements and for additional periods of up to fifteen years from the completion of such improvements, which improvements either (1) constitute a capital city project, as defined in subdivision (2) of § 32-600, receiving five million dollars or more in financial assistance from the authority, (2) are within the Adriaen’s Landing site, including the on-site related private development, or (3) constitute a capital city project, as defined in subdivision (2) of § 32-600, receiving three million dollars or more in financial assistance from the authority for purposes of creating downtown housing units with ancillary commercial or parking facilities for which project the authority makes a financial commitment in the year ending June 30, 2003.