The MuSun experiment will determine the μd capture rate (μ−+d → n+n+e) from the doublet hyperfine state d, of the muonic deuterium atom in the 1S ground state to a precision of 1.5%. Modern Effective Field Theories (EFT) predict that an accurate measurement of d would determine the two nucleon weak axial current. This will help in understanding weak nuclear interactions such as the stellar thermonuclear proton-proton fusion reactions, neutrino interactions and double beta decay. The experiment took place in the E3 beamline of Paul Scherrer Institute (PSI) using a muon beam. Muons were stopped in a cryogenic time projection chamber (cryo-TPC) filled with D2 gas. This was surrounded by plastic scintillators and multiwire proportional chambers for detecting the decay electrons and an array of eight liquid scintillators for detecting neutrons. The goal of this dissertation is to measure the dμd quartet-to-doublet fusion ratio (q : d) and μd hyperfine rate (qd) using the fusion neutrons from μ− stops in D2 gas. The dμd molecules undergo muon catalyzed fusion (MCF) reactions from the doublet and the quartet state with rates d and q, yield 2.45 MeV monoenergetic fusion neutrons. Encoded in the time dependence of the fusion neutrons are the dμd formation rates d, q and qd. Consequently, the investigation of the fusion neutron time spectrum enables the determination of these kinetics parameters that are important in the extraction of d from the decay electron time spectrum. The final results of this work yield q : d = 82.05 ± 4.01 and qd = 39.67 ± 0.4 μs−1. 1