From Science Daily:
In a study comparing amusics to people with normal musical ability, researchers used a brain imaging and statistical technique to measure the density of the white matter (which consists of connecting nerve fibers) between the right frontal lobe, where higher thinking occurs, and the right temporal lobes, where basic processing of sound occurs. The white matter of the amusics was thinner, which suggests a weaker connection. Moreover, the worse the tone deafness, the thinner the white matter.
To participate in a music perception test study online, check out http://www.delosis.com/listening developed by researchers at the University of Newcastle-upon-Tyne in England.
This site also has tests for rhythm and adaptive pitch: http://tonometric.com/adaptivepitch/