If a tenant brings in bedbugs who is responsible to pay for extermination?

Normally, the landlord is responsible for pest control and extermination. The exception is when the tenant is directly responsible, either due to negligence/carelessness or due to some intentional wrongful act (like a willing failure to follow hygience or cleaning instructions) for the infestation. However, to require the tenant to pay, the landlord would have to be able to prove in court (assuming the tenant does not pay voluntarily) that the tenant was in fact responsible for the bedbugs. The fact that they were found in 2 of 3 beds or that the premises had been tented the year before  does not necessarily by itself prove that the tenant was responsible--for example, the bedbugs could have come from an adjacent apartment, through air or heating ducts, etc. So while in theory a landlord can hold a tenant responsible for extermination costs, in practice it is very difficult unless the landlord can point to something the tenant definitively did causing the problem.

For example: say there is a bedbug problem and an exterminator is brought in; the exterminator directs the tenant to bag up clothing and bedding to allow extermination but the tenant refuses to do so--in that case, the landlord could hold the tenant responsible for later follow-up visits required by the failure of the first visit, since the landlord can show a specific action of tenant (refusing to bag up clothing and bedding) which caused the problem to persist.