They can insist all they want, what a court cares about is what they can prove. In multi-family property, landlords are always responsible for pest control. Always. Not just when it is convenient for them. They cannot charge you for this unless they can prove your conduct was the source of the infestation. So stop taking legal advice from your landlord and consider what you want to have happen. You may need to advise them to control the bugs, and if they do not, think about whether you want to continue living like this. Then read RCW 59 18 090. Elizabeth Powell
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Apparently, bed bugs can hitch rides in anything, not just furniture.
If the tenant causes the infestation, the tenant is responsible for the cost of pest control.
The issue for you and the landlord is who caused the infestation. Did you, your roommates, or one of your guests bring the bedbugs to your home? Or, were the bedbugs already in the unit when you moved in? Or, did the bedbugs crawl from one of your new neighbors?
Given that the statutes require the landlord to control pests in an apartment, the burden of proving who causes the infestation likely is that of the landlord.
If you want to confirm your suspicions, you can check with your neighbors to see if any of them is having a bedbug problem. If you know the tenants who moved out, perhaps you can ask them if there were bedbugs in the unit when the prior tenants left.