Justice Muralidhar was appointed as a Judge of High Court of Delhi on 29 May 2006. During his almost 14-year stint as a Judge of the High Court of Delhi, he pronounced various landmark judgments dealing with a variety of issues. He was later transferred as a Judge to the High Court of Punjab and Haryana where he was sworn in on 6 March 2020. As a judge he had deprecated the use of "my lord" and "your lordship" as a form of address in Court and had directed the Court's registry to append a note to the daily causelist for his Court requesting lawyers "to try and avoid addressing the judges as My Lord and Your Lordship”. The Collegium of the Supreme Court of India headed by Chief Justice of India S. A. Bobde in its meeting held on 12 February 2020 recommended the transfer of Justice Dr. S. Muralidhar from the High Court of Delhi to the High Court of Punjab and Haryana. The President of India accepted the recommendation of the Collegium of the Supreme Court of India and the transfer was notified on the night of 26 February 2020. The hurried "midnight" transfer of Justice Dr. S. Muralidhar was widely panned by lawyers, former judges, civil society members and the media across the country, and was considered to be a punitive measure by the government for the hearings conducted by the Division Bench of the High Court of Delhi headed by Justice Muralidhar into the inaction of police during the 2020 Delhi riots. During the Full Court Reference given by the High Court of Delhi on 5 March 2020 Justice Muralidhar spoke on the transfer giving details of the sequence of events. Sharing his views on "Judges" and "the act of judging" he had expressed that he doesn't subscribe to the view that "Judges perform a divine function" and that "jettisoning the prefix Lordship and even ‘Hon’ble’ is not a fetish. It is an acknowledgement of how mortal, temporal, and, if I may venture to add, fallible we are." He also has stated that he viewed the act of judging to take place in a "space that is both mediative and meditative" and that though there is a distinction between neutrality and impartiality, they are not antithetical. While he acknowledged that impartiality is an essential attribute and non-compromisable for a judge, he viewed neutrality, as per the Constitution, to require "the judge at all levels to be able to discern the weak from the strong litigant in terms of their capacities to access justice and lean on the side of the vulnerable in order to attempt to achieve equality of arms."