Right to counsel
While a state may have many statutes, court decisions, or court rules governing appointment of counsel for a particular subject area, a "Key Development" is a statute/decision/rule that prevails over the others (example: a state high court decision finding a categorical right to counsel in guardianships cases takes precedence over a statute saying appointment in guardianship cases is discretionary).
Legislation, Civil Contempt in Family Court
Any person subject to contempt for failure to comply with a child support order (or other order of the family court) is entitled to appointed counsel. N.Y. Fam. Ct. Act § 262(a)(vi). See also N.Y. Fam. Ct. Act § 453(b) (in child support enforcement proceedings, "The notice shall  advise the respondent of the right to counsel, and the right to assigned counsel, if indigent.") See In re Broome County Dep’t of Soc. Servs. v. Mitchell, 847 N.Y.S.2d 692, 693 (App. Div. 2007) (commitment of respondent to a jail term of six months was reversed because “he was not fully advised of his right to counsel upon his first appearance and was deprived of his right to counsel in later proceedings.”)
In other forms of civil contempt not handled in family court, the court must "inform the offender that he or she has the right to the assistance of counsel," and the statute states that the court has the discretion to appoint counsel if the offender is financially unable to do so. N.Y. Jud. Law § 770. While this sounds discretionary, one court has said that § Section 770 "require[s] the court to make a choice once indigency is found: either retain the power to punish the offender with a term of imprisonment by assigning counsel, or surrender that power by proceeding without assignment of counsel." Holmes v. Holmes, 454 N.Y.S.2d 22, 23 (App. Div. 1982) (remanding order of contempt so that court could make finding of indigency on issue of appointment of counsel); see also Clemens v. Clemens, 817 N.Y.S.2d 87, 88 (App. Div. 2006) (instructing the appointment of counsel under section 770 for a "defendant, appearing pro se, [who] asked for the assistance of assigned counsel on the ground that he was unemployed and had no income or assets").
If "yes", the established right to counsel or discretionary appointment of counsel is limited in some way, including any of: the only authority is a lower/intermediate court decision or a city council, not a high court or state legislature; there has been a subsequent case that has cast doubt; a statute is ambiguous; or the right or discretionary appointment is not for all types of individuals or proceedings within that category.
Appointment of Counsel: categorical Qualified: no