It's going to be difficult to help you out on this forum because you don't give enough details about your case to show why you want to sue the department. As a general rule, however, state agencies are immune to most civil suits. I would recommend contacting lawyers in your area who specialize in lawsuits against state and government agencies to determine whether you have an actionable claim.
This answer does not create an attorney/client relationship, and is only meant as a suggestion of how to proceed. Due to the facts unknown to the answerer, some or all of this advice may not be accurate. In order to receive a full answer to your questions, please consult privately with an attorney.
Sign up to receive a 3-part series of useful information and advice about child custody law.