A.k.a. the laughing gas. It is a colorless, with an almost unnoticeable metallic taste. Some WB users may know it as a mild anesthetic, for instance in dentistry.
Exposure to nitrous oxide causes short-term decreases in mental performance, audiovisual ability, and manual dexterity.
Because nitrous oxide is minimally metabolised in humans (with a rate of 0.004%), it retains its potency when exhaled into the room.
The creature mentioned in the question could "easily" create it from two of the most common gases already present in the air. In practice, it would go via the creation of ammonia, which is already there in a human-like body for urine production.
Direct oxidation of ammonia with a manganese dioxide-bismuth oxide
catalyst has been reported: cf. Ostwald process.
2 NH3 + 2 O2 → N2O + 3 H2O
Just coat the bladder of the creature with the right catalyst and allow the N2O to flow back in the blood stream and be either exhaled during respiration, or released via the sweat pores.
For a slightly less user-friendly experience, the creature could release instead Carbon Monoxide. This could be the result of a direct "digestion" of purified carbon in reduced oxygen, perhaps in an additional specialized stomach, just like a cow. We are thus talking about a creature that purifies graphite from sugars and farts carbon monoxide.
Carbon monoxide is tasteless colorless odorless, and, once inhaled, it sticks in the blood causing poisoning. The effect on human metabolism are quite severe, but at low dosage it may just cause a slight dizziness.