In this work we have theoretically studied the splittings experimentally observed in 5-methyl tropolone in the first excited singlet state, S-1. Tropolone shows a vibrational level splitting due to delocalization of the wave function over the symmetric potential energy double well in the proton-transfer coordinate. This splitting dramatically decreases when asymmetry is introduced. However, a noticeable splitting is observed in 5-methyltropolone internal rotational levels indicating a coupling between methyl internal rotational and proton-transfer degrees of freedom. We have developed a reduced-dimensionality model for the potential energy surface (PES), which maintains the main characteristics of the molecule and that can be fitted to electronic structure calculations. For this PES we have calculated stationary wave functions using a full quantum method. We have performed test calculations using different energy barrier heights in order to observe the splitting behavior for this kind of molecules. In order to fit our PES to the real system surface we have also performed an extensive set of ab initio calculations in the S-1 state using different methods. Finally we present a discussion about such electronic calculations, showing the present difficulties to obtain excited state potential energy surfaces with great accuracy beyond the Franck-Condon vertical excitation region.