Columbia University’s senate voted on Friday to approve a resolution that called for an investigation into the school’s leadership, accusing the administration of violating established protocols, undermining academic freedom, jeopardizing free inquiry and breaching the due process rights of both students and professors.

The university’s president, Nemat Shafik, has been under attack for her decision last week to summon the New York Police Department to campus, resulting in the arrest of more than 100 student protesters, and for her earlier congressional testimony, in which professors accused her of capitulating to the demands of congressional Republicans over free speech and the disciplining of students and professors.

The resolution, adopted by a vote of 62-14, with three abstentions, fell short of a proposal earlier in the week to censure Dr. Shafik, which many senators worried could be perceived as yielding to Republican lawmakers who had called for her resignation over her handling of antisemitism claims.

The senate resolution was based partly on a damaging report by the senate executive committee, which accused Dr. Shafik’s administration of engaging in “many actions and decisions that have harmed” the institution — including the hiring of an “aggressive” private investigation firm.

The report, which was discussed in Friday’s meeting, said that investigators harassed students and used “intrusive investigation methods,” which included “investigators’ attempt to enter student rooms and dormitories without students’ consent.”

Investigators, the report said, demanded “to see students’ phones and text messages with threats of suspension for noncompliance.”