If a rental house is infested with cockroaches, what does the halacha say about who is responsible for hiring an exterminator, the landlord or the tenant?
According to the Rabbi answering same question this site, if there are no specifications in the rental agreement then it depends:
If the house is uninhabitable due to the roaches, then the landlord has to pay.
If it's merely inconvenient then the tenant has to pay.
As to where to draw the line, he answers that if the infestation is so bad that a normal person would hire a Profesional Exterminator to deal with it then the landlord has to pay.
If it's a borderline case then the landlord does not have to pay, though it would be appropriate for him to share in the costs.
The Rabbi answering the question refers one to this pdf - on page 5 - where it discusses the halachic sources of Tenant vs. Landlord issues with sources.