By Sidney E. Morse and Samuel Breese. Published in New York by Sidney K. Morse and Samuel Breese, possibly in 1848-1850.
The copyright statement at the bottom of this map is 1844. However on March 16, 1847, William L. Greenly, acting Governor of Michigan, approved the act designating Lansing Township as the new seat of government. At the same time the site of the capital was called "Town of Michigan."(1) In April 1848, the state legislature changed the name to "Lansing."(2) Because the word "Lansing" on this map shows evidence of having been amended and is in a different font style, it may have been made after the 1848 name change. Both Detroit and Lansing have the State Capital symbol.
(1) History of Ingham and Eaton counties, Michigan, with illustrations and biographical sketches of their prominent men and pioneers. By Samuel W. Durant. Published in Philadelphia by D. W. Ensign & Co. in 1880, page 73.
(2) Greater Lansing History. http://www.lansing.org/about/history/