Well you need to qualify what types of tax dollars you are talking about. Capital gains do get taxed at a lower rate so if that is what you meant then yes some rich people do pay a lower tax rate than poor and middle class, but not all rich people earn money through capital gains either. If you are talking straight income tax rates then yes the rich are taxed at a higher rate.
There are two types of capital gains -- short term and long term. If you sell within 2 years, you pay the short term rate.
Short term tax rate = gains are treated as ordinary income, so it's dependent on the tax bracket you're in.
Long term tax rate = 0% to 20%, depending on your tax bracket. For 0% and 15% brackets, long tern capital gains is 0%. Anyone paying up to and including the 35% pays 15% on Capital gains. 39.6% tax bracket pays 20% on capital gains.
So, unless the wealthy individuals earn all their money from long term investments, they are paying a pretty hefty income tax already. If they are living off of long term investments, they are paying a smaller percentage on that money in taxes, but they are still paying more than similar investors in lower brackets and those who only earn regular income from wages.