We present an investigation of the globular cluster ( GC ) systems of NGC 3607 and NGC 3608 as part of the ongoing SLUGGS survey . We use wide-field imaging data from the Subaru telescope in the g , r , and i filters to analyse the radial density , colour and azimuthal distributions of both GC systems . With the complementary kinematic data obtained from the Keck II telescope , we measure the radial velocities of a total of 81 GCs . Our results show that the GC systems of NGC 3607 and NGC 3608 have a detectable spatial extent of \sim 15 , and 13 galaxy effective radii , respectively . Both GC systems show a clear bimodal colour distribution . We detect a significant radial colour gradient for the GC subpopulations in both galaxies . NGC 3607 exhibits an overabundance of red GCs on the galaxy minor axis and NGC 3608 shows a misalignment in the GC subpopulation position angles with respect to the galaxy stellar component . With the aid of literature data , we discuss several relationships between the properties of GC systems and their host galaxies . A one-to-one relation between the ellipticities of red GCs and the galaxy stellar light emphasises the evolutionary similarities between them . In our sample of four slowly rotating galaxies with kinematically decoupled cores , we observe a higher ellipticity for the blue GC subpopulation than their red counterparts . Also , we notice the flattening of negative colour gradients for the blue GC subpopulations with increasing galaxy stellar mass . Finally , we discuss the formation scenarios associated with the blue GC subpopulation .