but what you want to know isn't 'is it more likely that people with mental illness smoke than not'. what you want to know is 'is it more likely that people who smoke have mental illness or not'. otherwise... you get what is known as the 'base rate fallacy'.

nicotene addiction, tolerance, and withdrawal are in the DSM as mental disorders (rightly or wrongly). so smoking constitutes a mental disorder according to the DSM.

my guess would be that pets would lower your score because pets would contribute towards social support (which is negatively correlated with mental illness). i think... though... i could be wrong.