My wife needs to contact social services. Will they report me to immigration or do they not communicate?

Generally speaking, no. However, as a non-citizen you will always run the risk of being caught with immigration. However, you should keep mind you have a right to refuse voluntary departure and ask to see an immigration judge. You should be aware that ICE released a memorandum on November 10, 2014 listing three priorities for removal and detention. Priority level 1 includes people apprehended at the border while attempting to unlawfully enter the U.S., people who have felony convictions, and people who “pose a danger to national security.” Priority level 2 includes people convicted of a “significant misdemeanor” and people convicted of 3 or more misdemeanors.

They might report or not report, but they are very likely to check your immigration status with DHS, and that is where issues and red flags can arise. But whether you will be a priority to deport for DHS or not, that is a different matter.

Don't worry, Social Services will not report you to ICE or DHS and those two agencies rarely, if ever have any communication or talk to each other.