The principal issue underlying this appeal is whether petitioner was employed as a teacher in the public school system for the period from 1997 to 2003 and, thus, was entitled to credit in respondent. Petitioner joined respondent in 1971. In 1997, a program that petitioner had previously created evolved into Project Lead the Way (hereinafter PLTW) with a grant from the Charitable Venture Foundation (hereinafter CVF), a private foundation. In 1999, PLTW was officially incorporated as a not-for-profit corporation. From 1997 through 2002, petitioner served as PLTW’s director pursuant to an agreement between Hudson Valley Community College (hereinafter HVCC) and CVF whereby petitioner would manage PLTW at the school.
In 2002, petitioner applied for retirement and respondent thereafter approved petitioner’s application. Petitioner then retired and began receiving monthly benefits. However, in July 2006, respondent informed petitioner that it had made a preliminary determination that petitioner was not entitled to retirement credit from 1997 to 2003 because petitioner was employed by PLTW, not HVCC, during this period. Respondent subsequently made its final determination that petitioner was not entitled to any retirement credit for those years and that, because he was not an HVCC employee from and after February 2002, he was not entitled to a retirement incentive.* Respondent alternatively determined that petitioner was not entitled to retirement benefits for the subject period because he was not providing teaching services to HVCC within the meaning of *1268Education Law § 501. As a result, petitioner’s retirement benefits were substantially reduced and his payments were suspended until he repaid respondent for its overpayments.
Petitioner commenced this CPLR article 78 proceeding seeking, among other things, to annul and vacate respondent’s determination. Supreme Court granted the petition, finding that respondent acted arbitrarily and capriciously in reducing petitioner’s retirement benefits. Specifically, Supreme Court determined that petitioner was providing teaching services within the meaning of Education Law § 501 during the years in question and that respondent had failed to consider whether HVCC had a good faith basis for concluding that petitioner was its employee. Supreme Court therefore remitted the matter to respondent. Respondent now appeals from the entire judgment and petitioner cross-appeals from that portion of the judgment that remitted the matter to respondent rather than granting the relief requested in the petition.
Initially, we note that respondent is statutorily required to correct errors in retirement benefit payments and seek repayment of excess benefits already paid in order to ensure that the integrity of the public retirement system is maintained (see Education Law § 525 [3]; Matter of Galanthay v New York State Teachers’ Retirement Sys., 50 NY2d 984, 986 [1980]). In our view, since even an award of benefits erroneously made in good faith would affect the integrity of the public retirement system, the presence or absence of good faith on the part of the employer is irrelevant in determining whether an error occurred (see Matter of Galanthay v New York State Teachers’ Retirement Sys., 50 NY2d at 986). Additionally, because the contracting parties may not “agree to alter [their] rights and obligations . . . with respect to the retirement system” (Matter of Holbert v New York State Teachers’ Retirement Sys., 43 AD3d 530, 533 [2007]) and actual transactions between them determine whether an employer-employee relationship exists, this Court does not simply defer to the label they may assign their relationship (see id. at 532). Therefore, Supreme Court erred in directing respondent to make a determination as to whether HVCC had a good faith basis for considering petitioner to be its employee.
Moreover, we defer to respondent’s factual determination that an employer-employee relationship did not exist between petitioner and HVCC (see Matter of Wright [Central Transp., Inc. — Commissioner of Labor], 58 AD3d 988, 989 [2009], lv dismissed 12 NY3d 843 [2009]), as it was not arbitrary and capricious and had a rational basis in the record (see Matter of Maillard v New York State Teachers’ Retirement Sys., 57 AD3d *12691299, 1300 [2008], lv denied 12 NY3d 705 [2009]). Respondent reviewed, among other things, letters submitted on petitioner’s behalf, contracts between petitioner and HVCC and between HVCC and PLTW/CVF, the job description for director of PLTW at HVCC, petitioner’s monthly reports, articles and promotional materials for PLTW, PLTW’s tax returns and affidavits of individuals associated with respondent, CVF, PLTW and HVCC. These materials provided respondent with sufficient evidence to rationally conclude that petitioner was not an employee of HVCC. Notably, the contracts between HVCC and CVF (and subsequently between HVCC and PLTW) not only provided that CVF was solely responsible for payment of petitioner’s salary and other expenses, including “[a]ny and all termination and/or retirement benefits . . . that are due [petitioner] at the time of his termination/retirement from HVCC,” but also deprived HVCC of the right to decrease petitioner’s salary. Other evidence indicated that HVCC did not exercise sufficient control over petitioner to establish an employer-employee relationship (see generally Matter of Siepierski v New York State & Local Retirement Sys., 46 AD3d 1316, 1318 [2007]; Matter of Brosnahan v New York State Employees’ Retirement Sys., 174 AD2d 954, 955, 956 [1991], lv denied 78 NY2d 858 [1991]). The existence of evidence in the record supportive of an alternative decision that would also be reasonable does not render respondent’s determination irrational or require our interference (see Matter of Cooper v New York State Teachers’ Retirement Sys., 19 AD3d 724, 726 [2005]; Matter of Fernandez v New York State & Local Retirement Sys., 17 AD3d 921, 922 [2005], lv denied 5 NY3d 707 [2005]).
In light of the foregoing, respondent’s contention that it correctly determined that petitioner was not a “teacher” within the meaning of Education Law § 501 (4) and (19) is academic. We have considered the parties’ remaining claims, including petitioner’s allegations of due process violations, and find them to be without merit.
Cardona, PJ., Peters, Lahtinen and Malone Jr., JJ., concur. Ordered that the judgment is reversed, on the law, without costs, and petition dismissed.
This incentive resulted in petitioner being credited with an additional two years of service, for a total of 25 years, thus avoiding penalties that would otherwise reduce his benefits.