If ingested, the peppermint plant and its oil could indeed potentially cause harm to your cat. Cats are especially sensitive to peppermint oil, and effects such as gastrointestinal upset, central nervous system depression and even liver damage could occur if ingested in significant quantities. Some peppermint oil formulations also contain aspirin derivatives, which could result in additional toxicity. Furthermore, if inhalation of the volatile oil were to occur, aspiration pneumonia may be possible. Based on this, we would not recommend using peppermint leaves or oil in areas where your cat is allowed access.