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).
Litigation, Incarceration for Fees/Fines (incomplete)
Several Connecticut state courts have found a right to counsel for indigent defendants in civil contempt proceedings.
In Dube v. Lopes, 481 A.2d 1293, 1294 (Conn. Super. Ct. 1984) considered the Fourteenth Amendment right to counsel in state-initiated child support contempt proceedings established in Lake. v. Speziale, 580 F.Supp. 1318 (D. Conn. 1984), and extended it to contempt proceedings initiated by a private individual, as opposed to just those initiated by the state. The court reasoned that "[t]he result is the same and that is incarceration for failure to comply with a court order of support. Surely, the requisite state action which is necessary to trigger the due process clauses is present when a person is deprived of his physical liberty by the court." Dube, 481 A.2d at 1294. The Dube court expressly rested its holdings on both federal and state constitutional grounds, potentially insulating its effect from Turner v. Rogers, 564 U.S. 431 (2011). And because Dube focused on incarceration and the complexity of determining whether one can pay, this case would likely apply to all contempt orders for failure to pay a fine, fee, or other court ordered payment. (For a more in-depth exploration of the Dube decision, see Civil Contempt in Family Court.)
Then, in Emerick v. Emerick, 613 A.2d 1351, 1353 (Conn. App. 1992), a case involving child support, an appellate court cited to various federal appellate cases in addition to Lake v. Speziale to hold that "[t]he due process clause of the fourteenth amendment to the United States constitution guarantees the right to appointed counsel to any indigent civil contemnor who might be incarcerated," reasoning, "[t]his right to counsel is merely a logical extension of the right to counsel in criminal cases in which an accused is incarcerated." The court also held that the "trial court has an obligation to inform the potential contemnor of his right to appointed counsel to ensure that any waiver of the right to counsel is intelligent and competent."
The Emerick court reached this holding under both the Due Process Clause of the Fourteenth Amendment (citing Argersinger v. Hamlin, 407 U.S. 25  and Lassiter v. Dep't of Soc. Servs., 452 U.S. 18 ) and Conn. R. Super. Ct. Fam. § 25-63 (formerly, found at Section 484A of the Practice Book).
Subsequent to these cases, the U.S. Supreme Court held in Turner v. Rogers, that there is no categorical Fourteenth Amendment right to counsel in civil contempt proceedings where the opponent is neither the state nor represented by counsel. 564 U.S. 431 (2011). It held that an “unusually complex” case might require counsel but left for another day the question of whether cases involving the state or a represented party would require counsel. The holdings of Lake, Dube, and Emerick relating to state-initiated proceedings is likely intact, as that was not addressed by Turner, but the portion of Dube finding a right to counsel even in privately-initiated contempt proceedings may no longer be good law, at least in cases where the private party is not represented by counsel.
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: yes