At the Paul Scherrer Institut (PSI), we are developing a high-precision apparatus with the aim of searching for the muon electric dipole moment (EDM) with unprecedented sensitivity. The underpinning principle of this experiment is the frozen-spin technique, a method that suppresses the spin precession due to the anomalous magnetic moment, thereby enhancing the signal-to-noise ratio for EDM signals. This increased sensitivity enables measurements that would be difficult to achieve with conventional g - 2 muon storage rings. Given the availability of the 125MeV/c muon beam at PSI, the anticipated statistical sensitivity for the EDM after a year of data collection is 6×10^-23e·cm. To achieve this goal, it is imperative to do a detailed analysis of any potential spurious effects that could mimic EDM signals. In this study, we present a quantitative methodology to evaluate the systematic effects that might arise in the context of the frozen-spin technique utilised within a compact storage ring. Our approach involves the analytical derivation of equations governing the motion of the muon spin in the electromagnetic (EM) fields intrinsic to the experimental setup, validated through numerical simulations. We also illustrate a method to calculate the cumulative geometric (Berry's) phase. This work complements ongoing experimental efforts to detect a muon EDM at PSI and contributes to a broader understanding of spin-precession systematic effects.