Sound Shore Medical Center of Westchester, an affiliate of New York College of Medicine serving patients in the New Rochelle area, filed for bankruptcy protection, planning a sale to Montefiore Health System, Bloomberg News reported yesterday. The company, with about 2,000 employees, listed assets of $159.6 million and debts of $200 million in papers filed in Bankruptcy Court on Wednesday. Sound Shore said that it will continue business as usual pending the sale to Bronx, N.Y.-based Montefiore by the end of the year, subject to court approval. The center was formed in 1997, when Mount Vernon Hospital, Sound Shore Medical Center, Dorothea Hopfer School of Nursing and Schaffer Extended Care Center affiliated to create one of the largest private healthcare systems between New York City and Albany.