Most schools dont require any research at all from its medical students. The schools listed below are the only schools that require a thesis for graduation, but you can get away without doing one by doing a dual-degree program at most of the schools.
Albert Einstein College of Medicine of Yeshiva University
Duke University School of Medicine
George Washington University School of Medicine and Health Sciences
Mayo Medical School
University of California, San Diego, School of Medicine
University of New Mexico School of Medicine
University of Rochester School of Medicine and Dentistry
University of Washington School of Medicine
Yale University School of Medicine