We report on the composition of the Halley-family comet (HFC) 8P/Tuttle investigated with high-dispersion near-infrared spectroscopic observations. The observations were carried out at the ESO VLT (Very Large Telescope) with the CRIRES instrument as part of a multi-wavelength observation campaign of 8P/Tuttle performed in late January and early February 2008. Radar observations suggested that 8P/Tuttle is a contact binary, and it was proposed that these components might be heterogeneous in chemistry. We determined mixing ratios of organic volatiles with respect to H2O and found that mixing ratios were consistent with previous near infrared spectroscopic observations obtained in late December 2007 and in late January 2008. It has been suggested that because 8P/Tuttle is a contact binary, it might be chemically heterogeneous. However, we find no evidence for chemical heterogeneity within the nucleus of 8P/Tuttle. We also compared the mixing ratios of organic molecules in 8P/Tuttle with those of both other HFCs and long period comets (LPCs) and found that HCN, C2H2, and C2H6 are depleted whereas CH4 and CH3OH have normal abundances. This may indicate that 8P/Tuttle was formed in a different region of the early solar nebula than other HFCs and LPCs. We estimated the conversion efficiency from C2H2 to C2H6 by hydrogen addition reactions on cold grains by employing the C2H6/(C2H6+C2H$_{2})$ ratio. The C2H6/(C2H6+C2H$_{2})$ ratio in 8P/Tuttle is consistent with the ratios found in other HFCs and LPCs within the error bars. We also discuss the source of C2 and CN based on our observations and conclude that the abundances of C2H2 and C2H6 are insufficient to explain the C2 abundances in comet 8P/Tuttle and that the abundance of HCN is insufficient to explain the CN abundances in the comet, so at least one additional parent is needed for each species, as pointed out in previous study.