Yes you probably overstepped. You are not this child's parent and you might not be getting the full picture from the kid.
There was nothing CPS could have or would have done and I will be surprised if they do anything in your case either..to me CPS honestly has far more serious matters to focus on than this..I would rather they help the kid being beaten or starved personally but I get that your heart was the in the right place.
Does your state have a program like this? http://www.superiorcourt.maricopa.gov/JuvenileProbation/Probation/CUTS.asp
My biggest issue is that you called CPS..something very serious IMO based on the word of a 13ish year old? Yeah that is a big concern to me..kids lie, exaggerate and manipulate the facts to try to suit their needs and purposes..I don't believe it is good or appropriate to call in serious authorities over some statements from a kid. I would need more details and actual verification of what is going on before I considered calling the police.
I get that you are trying to help the child but you don't have the right to police everyone else and what they do or how they do it.
CPS IMO is very much the wrong place to go to..that is for serious serious stuff..school district or local truancy program for your city/state/county would be more appropriate but I do ask..what are the ages regarding education and homeschooling in your state? Before you called did you review them to find out if the mother is even doing something that would be illegal or go against the laws for homeschooling in your state?
I don't know about other states, but the CPS in NY are so overwhelmed with cases of severe abuse that require investigating (beatings; sexual abuse; starving; etc.) the last thing they need is a call to investigate a child not going to school.. While they're at the home investigating your former nanny, some other child could be in the position of being repeatedly sexually abused or beaten to death..

Your avenue of intervention - if you truly believe this is happening as you are stating - should have been the state board of education..
This is not the type of neglect that should be tossed in the laps of the already overworked CPS employees who are trying to save childrens lives or remove them from a home where they are being sexually abused and/or are going without food..
I suppose they're mandated to investigate it now (they would be in NY - within 48 hours) and I find that very upsetting.. They will be checking on your former nanny while another child is in extreme danger - and could possibly die..

Bad call - in my opinion..