First, this link will take you to a map: Martin Township, 1913 Standard Atlas of Allegan County from the UofM Digital Library. Scroll to the lower left corner to sections 29-32.
The solid north/south rail line that is labeled Grand Rapids & Indiana is now part of the Grand Elk, still in service. You probably know that.
The dashed north/south line that runs through Martin (and is now a power line) was the Michigan United Railway (Interurban) line from Kalamazoo to Grand Rapids, built in 1915 and abandoned in 1928. It is labeled on the map as Michigan & Chicago (proposed).
The solid east/west line crossing in the north portion of section 32 gets a little foggy. It was built between Montieth (Sta) on the GR&I and Allegan by the Mansfield, Coldwater & Lake Michigan in 1871, and between Montieth (Sta) and Dundee by the new owners Allegan & Southeastern in 1877. It went through several owners and names in a short span: 1883: Michigan & Ohio, 1887: Cincinnati, Jackson & Mackinaw, 1897: Toledo & Milwaukee, then Detroit, Toledo & Milwaukee. The line was leased by the Cincinnati Northern in 1899, then leased again jointly by the LS&MS (operating the eastern half) and Michigan Central (operating the western half) in 1905. In 1913, the portion between Battle Creek and Allegan was sold to Michigan & Chicago (Interurban), which became part of the Michigan United Railway (Interurban) under several similar but different names. It was abandoned beteeen Hooper Station (in the SW corner of section 36) and Allegan in 1928.
The junction at Montieth Station is clear on the map. The junction between the Interurban lines just west of Montieth Station was known as Montieth Junction.
This construction, ownership and abandonment information was taken from Michigan Railroad Lines, Volumes 1 and 2 by Graydon Meints. Thanks again Don for all of your research.