I would be quite surprised if that were true. The illegal immigrants pay a higher tax rate because as some of the poorest people in the country, they are the most affected by regressive taxation (primarily sales taxes, according to this study). As income increases, the distortion from these regressive taxes should decline so the effect of the higher tax brackets that the wealthy are in will become dominant.

Edit: I don’t have time to find data for every state, but here’s federal data from Pew. Federal taxation is progressive and the share of income paid by the highest earners is many times larger than the share paid by the lowest earners.