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Great question! I am personally concerned about pesticide and chemical use around my family, so I understand your concern.
In general, the relationship between the landlord and tenant is contractual, and the first place to look for answers to questions about your relationship is any written lease. If your question is not answered there, then it may be difficult to answer your question without further legal research.
There are many legal clinics available to help tenants with their legal questions. Try calling the University of Cincinnati Tenant Information Project (linked below) for advice.
All of this said, the best solution is if you can explain your concerns to your landlord and work out a mutually agreeable solution.