From the Marshall Public Library website:
In 1915, the Walter Burdick Chapter of the Daughters of the American Revolution sought to include the question of a public library on the April 1916 ballot. A newspaper campaign was started to create "favorable sentiment" for all the reasons why a library would benefit the community.
The Daughters campaign was successful and the option to vote for a free public library was added to the April 1916 election ballot. The community overwhelming voted in favor of a public library.
The grand opening for the library was October 1916. The first location was the second floor of the Claypool Building on the southwest corner of 5th and Main Street (now Archer Avenue). The only access to the library was by way of an outdoor staircase on the north side of the building. It is now location [sic] to Old National Bank. 
From personal correspondence on Facebook with the library on October 11, 2016:
October 4th was the official first day. We just celebrated that date last week and served cake in front of the library. We had a great turnout - about 400 people!