We have devised a semiclassical procedure based on the Makri-Miller [J. Chem. Phys. 91, 4026 (1989)] model for calculating the eigenvalue splitting in many-atom systems and have used it to Calculate the ground-state splitting in several isotopomers of malonaldehyde. A potential-energy surface that includes all twenty-one vibrational degrees of freedom was constructed based on the available theoretical and experimental information. The results for calculations in which all atoms are allowed full three-dimensional motion are in good agreement with the experimentally measured values. Restricting the molecular motion to a plane leads to an increase in the splitting due to a decrease in the average height and width of the barrier to tunneling when the molecule is not allowed to vibrate transverse to the molecular plane. Low energy mode-specific excitations were used to study the sensitivity of the splitting to the motions of heavy atoms. The results show that the heavy atom motions have significant influence on the tunneling. This study demonstrates that simple semiclassical methods can be used to treat proton tunneling in large systems.