Global Warming occurs because gases in the atmosphere interfere with radiation of "excess" heat to space. These gases are called "greenhouse gases". Ozone itself is a greenhouse gas, as is carbon dioxide and water vapor. Any molecule with three or more atoms will be a greenhouse gas.
The hole in the ozone layer is a natural, repeating occurrence. The primary reason for the thinning of this the ozone layer is due to the sun not being able to create more ozone over the poles for a few months each year. The angle of the planet in relation to the sun determines the location and size of this miss label thin area called a hole. many people believe that man may also play some part in the thinning that occurs naturally.
The two phenomenon are unrelated, except by the addition of new / more compounds to the atmosphere, by both Nature and Man.
Man's contribution to global warming and the depletion of the ozone layer are caused by pollution. This warming started over 6000 years ago and has risen almost 11 degrees. 0.2 of this since man has started burning fossil fuels. The ozone hole has always occurred as far as we can tell. The hole appears to have been the largest in the mid 1800's due to solar activity during that era.
It should be noted that over the past 6000 years we have seen a 11 degree C rise. In the past 150 years we have seen a 0.6 degree rise. In the past 10 years we have seen a slight cooling. 1998 was the warmest year on record and cooling has been quietly observed by NASA in our oceans.
If there is any real warming due to man, this would tend to show up as consistent global warming. The two warmest years on record are 1999 and then 1938 in recorded history. The trend is not for warmer years.
If should be also pointed out that recorded history is less then 150 years. Lastly, climate change has occurred for millions of years. We are in a very natural cycle that we have seen over and over again.