Are landlords liable for treating bed bug infestations?

[Stephan Mayer]

Dear fellow investors:

I received a $700 bill from my property management to treat a bed bug infestation in a small duplex.
Can I hold the renters responsible for this bill - or at least part of it?
I've owned the building for ~1.5 years; one renter came with the property when I purchased it, the other has been there for ~1 year. It's a clean building and to the best of my knowledge there has been no such infestation before. By deduction one of the renters must have introduced he bed bugs but they blame each other.
Thanks in advance for sharing your relevant experience with such situations and your thoughts.