Answer:
It depends on two things..which can vary from state to state
1.The landlord tenant laws in your state...
2. The lease agreement.
Some States require that the landlord be responsible for all forms of pest control (ie) roaches,rats,mice,bees,bed bugs,ants,spiders,ect ect..
Some States only require the landlord to insure that a rental unit is free from all pests before renting the unit and then any further pest control is the responsibility of the tenant...
Lease agreements can also have stipulations for pest control as well according to the laws of the state....(ie) A landlord may be responsible for the control of mice,rats and termites but may not be responsible for roaches,bed bugs and ants...
So check your lease and the laws of your state....