You need to get a humidifier. You air is too dry and that can be a danger to your and your cat's mucus membranes. It also causes static. Check out the Wikipedia entry for humidifier. Good luck.
You might want to think about what shoes / footwear you have on at home and what the floors and floor coverings are. As well as air conditions things like under floor cabling, panel floors and synthetic carpets can add to static we humans build up, as can the material the soles of our shoes are made of as this can conduct or form a barrier depending on what they are. I have always been prone to building up static and clothes always cling and give shocks, particularly synthetics. Mouse has had a few little shocks when I have touched him and he gets a little start: I think he has learned it is not a deliberate thing and not something that happens all the time so he isn't afraid of me - which would be devastating. When I go through phases where I seem to get / give more shocks I try to touch something that absorbs some of the electricity before I go stoke Mouse.