The carbon compounds that you don't want in the water (bacteria, flakes of skin, oils, sunscreen, etc.) are oxidized into carbon monoxide, carbon dioxide, and other gasses. I suppose you could calculate this amount from the amount of oxidizer you put in the pool, but that's going to be negligible compared to the amount of carbon dioxide that's generated heating the pool and running the pumps.
To calculate the carbon dioxide generated by any pool you need to know how much energy it uses, and even then it's not so clear cut. Even with a pool powered 100% by hydroelectricity, you'd still have to account for the carbon dioxide that's produced by the natural oxidation of organic materials trapped in artificial dams.
Overall, pools are a lot like cars. CO
2 emissions are significant.
Without begrudging anyone their favorite swimming pools, I'd be interested to see reports too... I imagine a lot of energy could be saved with alternative heating sources, and improved filtration systems.
Here's the PG&E swimming pool page:
http://www.pge.com/res/rebates/pumps_motors/pool_tips/index.html