(CNN) — A bipartisan pair of senators will introduce legislation on Wednesday that aims to implement new ethics standards on the Supreme Court, though it would still grant the high court extensive power to police itself.

The “Supreme Court Code of Conduct Act,” to be introduced by Independent Maine Sen. Angus King, who caucuses with Democrats, and Republican Sen. Lisa Murkowski of Alaska, would require the nation’s highest court to enact its own code of conduct within a year of the bill passing.

Under the legislation, the court would have the power to “initiate investigations as needed to determine if any Supreme Court justices or staff may have engaged in conduct that is prejudicial to the administration of justice or that violates other federal laws or codes of conduct.”

The legislation would also require the court to lay out the rules on its website, name an official to handle complaints about violations of those rules (which could come from anyone including the public), and then require that official to publish an annual report chronicling actions taken in response to any of those complaints.

It is unclear if the legislation will garner bipartisan support, as Republicans have generally not expressed the same level of concern as Democrats in regard to ethics regulation at the Supreme Court.

The Supreme Court in recent months has been under pressure to adopt a formal code of ethics, similar to one that applies to lower-court federal judges and provides enforcement mechanisms for policing conflicts involving transactions or business relationships with lawyers or others who come before the court.

Public trust in the court has tumbled down in recent years, according to Gallup, and recent reports of potential business relationships involving Justices Clarence Thomas and Neil Gorsuch have intensified calls for greater ethical oversight.

Senate Judiciary Chairman Dick Durbin, an Illinois Democrat, recently asked Chief Justice John Roberts to testify at an upcoming hearing on Supreme Court ethics, a request that Roberts declined on Tuesday, instead releasing a new statement signed by all nine justices that is meant to provide “clarity” to the public about the high court’s ethics practices.

The newly drafted statement by the court notes that the justices “today reaffirm and restate foundational ethics principles and practices to which they subscribe in carrying out their responsibilities as Members of the Supreme Court of the United States.”

Without addressing Durbin’s specific concerns over ethics, Roberts simply attached a “Statement on Ethics Principles and Practices,” to which he said, “All of the current Members of the Supreme Court subscribe.”

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