Yes. St. Louis does have a municipal ordinance called the "Smoke Free Air Act," which you can find in the St. Louis City Revised Code Chapter 11.31
. You can read the full text of this law in the link just given. But the section of this law which would be most applicable to office buildings would be Section 11.31.050
which basically prohibits smoking in places of employment and states as follows:
11.31.050 Prohibition of smoking in places of employment.
A. Smoking shall be prohibited in all enclosed facilities within places of employment in the City of St. Louis except where smoking is not regulated as defined in Section 11.31.070. This includes common work areas, auditoriums, classrooms, conference and meeting rooms, private offices, elevators, hallways, medical facilities, cafeterias, employee lounges, stairs, restrooms, vehicles, and all other enclosed facilities.
B. This prohibition on smoking shall be communicated to all existing employees by the effective date of the ordinance codified in this chapter and to all prospective employees upon their application for employment.
I hope this answers your question.