We present evidence that electrical transport studies of epitaxial p-type GeMn thin films fabricated on high-resistivity Ge substrates are severely influenced by parallel conduction through the substrate, related to the large intrinsic conductivity of Ge due to its small band gap. Anomalous Hall measurements and large magnetoresistance effects are completely understood by taking a dominating substrate contribution as well as the measurement geometry into account. It is shown that substrate conduction persists also for well-conducting, degenerate, p-type thin films, giving rise to an effective two-layer conduction scheme. Using n-type Ge substrates, parallel conduction through the substrate can be reduced for the p-type epilayers, as a consequence of the emerging pn-interface junction. GeMn thin films fabricated on these substrates exhibit a negligible magnetoresistance effect. Our study underlines the importance of a thorough characterization and understanding of possible substrate contributions for electrical transport studies of GeMn thin films.