The material damping in carbon fibre-reinforced polymers can relate to the material's damage condition. An improved understanding of the relationship between the presence of transverse matrix cracks and material damping is promising for applications in structural health monitoring. The present study investigates the subject with coupon-level specimens in a free-decay experiment, capturing the velocity response with a laser Doppler vibrometer. Analysing the decay signal with a curve-fitting approach enables quantifying the amplitude-dependent material damping of both pristine and pre-damaged specimens. In contrast to related studies, the results indicate no correlation between the investigated transverse matrix cracks and the material damping in the investigated first bending mode. However, it was found that the layup configuration and small variations in the specimen thickness strongly influence the dynamic response.