He was appointed Auxiliary Bishop of the Archdiocese of Boston on November 21, 1995 and consecrated a month later on December 27, 1995. Pope John Paul II appointed Murphy to succeed the late Bishop James T. McHugh to head the Diocese of Rockville Centre on June 26, 2001. He was installed as the Fourth Bishop of Rockville Centre on September 5, 2001. Murphy is also a past member of the Board of Trustees of The Catholic University of America. He signed the document Evangelicals and Catholics Together. In 2007 he was appointed the head of the Domestic Policy Committee of the U.S. Conference of Catholic Bishops, which advises the U.S. Catholic church to shape positions on issues ranging from welfare to health care to the death penalty. Murphy has a reputation as an orthodox church conservative although non-confrontational. He is fluent in English, Italian, French and Spanish.
Allegations of protecting abusive priests
Bishop Murphy has denied that he helped to protect abusive priests while he was second in command at the Roman Catholic Archdiocese of Boston, before coming to Long Island in 2001. Murphy's denials contradicted a July 2010 report by the Massachusetts attorney general that stated that Murphy "placed a higher priority on preventing scandal and providing support to alleged abusers than on protecting children from sexual abuse." The report also stated: "There is overwhelming evidence that for many years Cardinal Law and his senior managers had direct, actual knowledge that substantial numbers of children in the Archdiocese had been sexually abused by substantial numbers of priests.” The Catholic League defended Murphy, contending, amongst other things, that the allegations were unfounded and that Massachusetts did not require clergy at the time to report abuse; and the internal pastoral response was at the time the norm in all religions. The League also praised Murphy’s leadership and actions on issues involving sexual abuse since his appointment to the Diocese of Rockville Centre in September 2001. Bishop Accountability.Org says Murphy is "a key figure in the sexual abuse crisis, both because of his earlier role in the Boston archdiocese and because of conditions in Rockville Centre." Monsignor Alan J. Placa, a Rockville Centre diocesan priest, was cleared by the tribunal of the Diocese of Albany, the home diocese of the complainant, of allegations made against him in June 2002. The decision was subsequently confirmed by the Congregation for the Doctrine of the Faith, which instructed Murphy "to do what we can to restore his good name.”
Renovation of bishop's quarters
reporter Jimmy Breslin criticized Murphy for spending more than US$5 million on renovations for St. Agnes Cathedral that included the creation of a private residence for himself. Murphy took over the third floor of an old convent that was being renovated to accommodate six nuns and requested them to relocate. The convent had room for 37 apartments. "The sisters, I think, were disappointed," Murphy said, "but a disappointment they expressed with great generosity. They understood my dilemma." Murphy deemed his current living quarters in the cathedral rectory as unsatisfactory because they lacked privacy, and that a separate donated house was not large enough to entertain visiting prelates. After construction started, the original estimate of $500,000 for construction and furnishings increased to $800,000. Murphy then invited another Newsday reporter and photographer to review the accommodations. They reported that the suite consisted of a lavishly decorated living room, a new fireplace with an oak mantel, a kitchen with top-of-the-line appliances, a marble bathroom, a bedroom and study for the bishop's secretary, a separate suite called "the cardinal’s suite," and a public wing with a fourth bedroom for visiting laity. Murphy believes that the cost was justified since the new bishop's residence can serve simultaneously as a residence for the bishop, his secretary, the cardinal, and other visiting laity. Shortly after the story about the new residence broke, the local Catholic Charities branch operating in the Diocese of Rockville Centre announced that it was terminating a $1.1 million home care program that had served 500 poor, mentally ill people on Long Island. Catholic Charities attributed its decision to “mounting expenses.” Kate Bishop, the program’s coordinator stated to the press: “It’s interesting that our deficit is about the same amount as what the church is spending on the kitchen appliances and Oriental rugs in the residence.” “Our mission is to serve people who are marginalized and disenfranchised. For them to turn around, with no notice, and end the program, is horrible.”
Discontent amongst diocesan priests
In October 2003, 52 priests requested a meeting with Murphy after sending a letter that spoke of a "general malaise and even an abiding anger" within the diocese, "a fairly widespread dissatisfaction with the way you have related to some clergy and the laity" and "a certain lack of confidence in your pastoral leadership." Issues raised included Bishop Murphy's management style, the excessive cost of renovating a diocesan building into his personal residence, ongoing concerns of how he handled the sexual abuse scandal, and his ban against the 1,000 member reform group Long Island Voice of the Faithful, which has asked Murphy to resign, from meeting on church property.
Catholic school closings
On December 5, 2011, Murphy made the decision to close six Roman Catholic elementary schools on Long Island. Students of Saint Catherine of Sienna School held a protest on December 21, 2011. Podium speakers stated that several munificent parishioners offered to make sizable donations to meet the relatively small financial shortcomings of the parish school, which they claimed Murphy would not entertain. Additionally, parishioners at the protest alleged that 68 students enrolled in Saint Catherine of Sienna’s nursery and pre-kindergarten programs were excluded from the Bishop’s financial analysis.