Private law

regulations that deal with interpersonal disputes

Private law is that part of a legal system which is part of the jus commune that involves relationships between individuals, such as the law of contracts or torts, as it is called in the common law, and the law of obligations as it is called in civilian legal systems. It is to be distinguished from public law, which deals with relationships between natural and artificial persons (i.e., individuals, business entities, non-profit organizations) and the state including regulatory statutes, penal law and other law that effects the public order.
See more at Wikipedia.org...

For the bill proposed by an individual member of the legislature instead of the government, see Private Member's Bill. A private bill is an act considered or acted upon by a legislature that helps a single individual, group of individuals, or corporate entity, by from another law, granting a unique benefit, or relieving the individual from legal responsibility for some allegedly wrongful act.
See more at Wikipedia.org...

Law which regulates the relationships between individuals. Family, commercial and labor law are examples of private law because the focus of those kinds of laws is the relationships between individuals or between corporations or organizations and individual, with the government a bystander. - (read more on Private law)