Pest Control is the LL's responsibility UNLESS it is a SFH and if it is a SFH the LL can include some pest control responsibilities in the lease. Which only makes logical sense. In an apartment complex roaches could come from a "wall or floor neighbor", whereas in a SFH roaches are directly cause by the tenant.
FYI...Recent learning for me...There are two types of "german roaches". Actually the one inside are german roaches, but there is a roach that looks just like the inside one but lives outside. The inside ones can not live outside and the outside ones can not live inside. So the next time a tenant tries to tell you that the Roach infestation is because the backdoor is warped or a window doesn't shut completely WRONG!!!