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
There is a right to counsel for indigent defendants in child support contempt cases if incarceration is a possibility (Conn. Gen. Stat. Ann. § 46b-231[m] [child support contempt]; see also Martocchio v. Savoir, 23 A.3d 1282, 1286 at n.2  [denying appointment of counsel under the rule because “the [trial] court stated, on the record, that the plaintiff did not face incarceration as a possible result of the proceeding …”]) and for all family court cases where incarceration is a possibility. Conn. R. Super. Ct. Fam. § 25-63. Section 46b-231(m)(7) requires the court to inform the child support obligor of their right to counsel, and if the obligor indicates they cannot afford counsel, the court "shall conduct a hearing to determine if the obligor is indigent."
Moreover, in Kennedy v. Kennedy, the court held that:
[A] court's failure to advise a party of the right to counsel in a contempt proceeding in which he faces potential incarceration, and in the event he is indigent, to court-appointed counsel, is fatal to the finding of contempt and any order related thereto .... Moreover, a waiver of a right to counsel 'should be clearly determined by the trial court, and it would be fitting and appropriate for that determination to appear on the record.
847 A.2d 1104, 1107-08 (Conn. App. Ct. 2004) (citation omitted).
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