N.Y. Comp. Codes R. & Regs. tit. 22, § 1015.15 – Contingent fees in claims and actions for personal injury and wrongful death.

(a) In any claim or action for personal injury or wrongful death, other than one alleging medical, dental or podiatric malpractice, whether determined by judgment or settlement, in which the compensation of claimant's or plaintiffs attorney is contingent, that is, dependent in whole or in part upon the amount of the recovery, the receipt, retention or sharing by such attorney, pursuant to agreement or otherwise, of compensation which is equal to or less than that contained in any schedule of fees adopted by this department is deemed to be fair and reasonable. Unless authorized by a written order of a court as hereinafter provided, the receipt, retention or sharing of compensation which is in excess of such scheduled fees shall constitute the exaction of unreasonable and unconscionable compensation in violation of the applicable provisions of the Rules of Professional Conduct (section 1200.0 of this Title) or, with respect to conduct before April 1, 2009, the former Code of Professional Responsibility.
(b) The following is the schedule of reasonable fees referred to in subdivision (a) of this section, either:
1. (1) 50 percent on the first $1,000 of the sum recovered;
2. (2) 40 percent on the next $2,000 of the sum recovered;
3. (3) 35 percent on the next $22,000 of the sum recovered;
4. (4) 25 percent on any amount over $25,000 of the sum recovered; or
  SCHEDULE B
  A percentage not exceeding 33 ⅓ percent of the sum recovered, if the initial contractual arrangement between the client and the attorney so provides, in which event the procedure hereinafter provided for making application for additional compensation because of extraordinary circumstances shall not apply.
  Compensation of claimant's or plaintiffs attorney for services rendered in claims or actions for personal injury alleging medical, dental or podiatric malpractice shall be computed pursuant to the fee schedule contained in Judiciary Law, section 474-a.
SCHEDULE A
(c) Such percentage shall be computed by one of the following two methods to be selected by the client in the retainer agreement or letter of engagement:
1. (1) on the net sum recovered after deducting from the amount recovered expenses and disbursements for expert testimony and investigative or other services properly chargeable to the enforcement of the claim or prosecution of the action; or
2. (2) in the event that the attorney agrees to pay costs and expenses of the action pursuant to Judiciary Law section 488(2)(d), on the gross sum recovered before deducting expenses and disbursements. The retainer agreement or letter of engagement shall describe these alternative methods, explain the financial consequences of each, and clearly indicate the client's selection. In computing the fee, the costs as taxed, including interest upon a judgment, shall be deemed part of the amount recovered. For the following or similar items there shall be no deduction in computing such percentages: liens, assignments or claims in favor of hospitals, for medical care and treatment by doctors and nurses, or self-insurers or insurance carriers.
(d) In the event that claimant's or plaintiffs attorney believes in good faith that schedule A, in subdivision (b) of this section, because of extraordinary circumstances, will not give the attorney adequate compensation, application for greater compensation may be made upon affidavit with written notice and an opportunity to be heard to the client and other persons holding liens or assignments on the recovery. Such application shall be made to the justice of the trial part to which the action had been sent for trial; or, if it had not been sent to a part for trial, then to the justice presiding at the trial term calendar part of the court in which the action had been instituted; or, if no action had been instituted, then to the justice presiding at the trial term calendar part of the Supreme Court for the county in the judicial department in which the attorney making the application has an office. Upon such application, the justice, in his or her discretion, if extraordinary circumstances are found to be present, and without regard to the claimant's or plaintiffs consent, may fix as reasonable compensation for legal services rendered an 'amount greater than that specified in schedule A, in subdivision (b) of this section; provided, however, that such greater amount shall not exceed the fee fixed pursuant to the contractual arrangement, if any, between the client and the attorney. If the application be granted, the justice shall make a written order accordingly, briefly stating the reasons for granting the greater compensation; and a copy of such order shall be served on all persons entitled to receive notice of application.
(e) Nothing contained in this section shall be deemed applicable to the fixing of compensation for attorneys representing infants or other persons, where the statutes or rules provide for the fixation of such compensation by the court.
(f) Nothing contained in this section shall be deemed applicable to the fixing of compensation of attorneys for services rendered in connection with collection of first-party benefits as defined in article XVIII of the Insurance Law.