Cats groom themselves to keep clean, and may ingest large amounts of oil during grooming. Neem oil is not poisonous to cats, but it can still cause vomiting and diarrhea. However, it can cause some skin irritations and allergic reactions in cats. If your cat's skin becomes irritated, red or itchy, stop using the neem oil immediately.
Contact your veterinarian for advice as soon as possible if you think your cat may have ingested neem oil.