I suspect that my roommate has been using insecticides in my bedroom, living room, or kitchen.
How can I check or test this?
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If you have a particular location in the room where you suspect they may have been used, you could try releasing some live bugs there (ones that are moderately welcome indoors), eg some jumpy spiders. If they quickly die, that would indicate insecticide use.
Obviously you would ensure any bugs released are in good health to start with, and release several to get a more reliable result.