The zero-truncated Poisson (ZTP) distribution is used to model count data in situations where zero values cannot be observed. It has been extensively researched for parameter estimation, especially concerning the construction of confidence intervals. However, methods for hypothesis testing across multiple ZTP populations remain underdeveloped. This study proposes two hypothesis testing procedures for comparing two ZTP parameters: the ZTP C-test, based on a conditional distribution approach, and the ZTP E-test, relying on numerical p-value approximation. Both methods extend techniques used for the standard Poisson case. Our results show that although the ZTP E-test requires more intensive computation, it consistently achieves higher power than the ZTP C-test. Furthermore, the ZTP E-test attains a given power level with smaller sample sizes, highlighting its efficiency despite the greater computational cost. These results advance the development of hypothesis testing methods for the ZTP parameter, which arises frequently in various fields where zero counts are inherently absent.