The licensing statute is reproduced below. My interpretation would include investigations into the background of persons. Though the word "background" is not found in the text of the statute itself, the phrase, "...conduct, honesty, efficiency, loyalty or activities of employees, agents, contractors, and sub-contractors," seems to cover those research activities conducted by a background checking organization.
NY Statutes GBA §71. Definitions
1. "Private investigator" shall mean and include the business of private investigator and shall also mean and include, separately or collectively, the making for hire, reward or for any consideration whatsoever, of any investigation, or investigations for the purpose of obtaining information with reference to any of the following matters, notwithstanding the fact that other functions and services may also be performed for fee, hire or reward; crime or wrongs done or threatened against the government of the United States of America or any state or territory of the United States of America; the identity, habits, conduct, movements, whereabouts, affiliations, associations, transactions, reputation or character of any person, group of persons, association, organization, society, other groups of persons, firm or corporation; the credibility of witnesses or other persons; the whereabouts of missing persons; the location or recovery of lost or stolen property; the causes and origin of, or responsibility for fires, or libels, or losses, or accidents, or damage or injuries to real or personal property; or the affiliation, connection or relation of any person, firm or corporation with any union, organization, society or association, or with any official, member or representative thereof; or with reference to any person or persons seeking employment in the place of any person or persons who have quit work by reason of any strike; or with reference to the conduct, honesty, efficiency, loyalty or activities of employees, agents, contractors, and sub-contractors; or the securing of evidence to be used before any authorized investigating committee, board of award, board of arbitration, or in the trial of civil or criminal cases. The foregoing shall not be deemed to include the business of persons licensed by the industrial commissioner under the provisions of §24-a or subdivision 3-b of §50 of the Workers' Compensation Law or representing employers or groups of employers insured under the Workers' Compensation Law in the State Insurance Fund, nor persons engaged in the business of adjusters for insurance companies nor public adjusters licensed by the Superintendent of Insurance under the Insurance Law of this State.