The Constitution demands the chief justice not cast any tie-breaking vote in the Senate
https://m.washingtontimes.com/news/2020/jan/21/the-constitution-demands-the-chief-justice-not-cas/
As the impeachment trial of the president begins, fidelity to the U.S. Constitution demands the chief justice decline any invitation or inclination to break a tie vote should one occur; not only does the Constitution not grant him such power but, in fact, the Constitution grants that exclusive power and authority to a different constitutional officer.
Hypotheticals and wishful thinking currently abound in certain quarters concerning the role of Chief Justice John Roberts in presiding over the impeachment trial. Such speculation usually involves the chief justice being called upon to break a tie vote on a procedural matter (such as calling witnesses or which witnesses to allow), together with a certain desired outcome depending upon where one stands in the political spectrum.
Notwithstanding the siren songs of the Washington establishment and media hoping the chief justice will cast a tie-breaking vote against the president’s interests, the chief justice has a chance to demonstrate judicial restraint and the primacy of the Constitution if called upon to cast such a vote. Such action is not accomplished through impartially casting a tie-breaking vote in favor of one political party over the other, or in favor of the House managers or the president. Instead, to be true to the Constitution, the chief justice must refuse to cast any tie-breaking vote whatsoever.
With respect to an impeachment trial of the president, the only authority the Constitution grants a chief justice is to preside over the trial; the Constitution does not grant him any vote in the process. And if Chief Justice Roberts were to cast a tie-breaking vote in the Senate, not only would he be assuming a power not granted to him by the Constitution, but he would, in fact, be usurping and violating the right and prerogative expressly granted to another person by the Constitution.
The Constitution is clear and unequivocal: The power to cast a tie-breaking vote in the Senate is explicitly granted to one and only one person, namely, the president of the Senate. Such grant of power and authority is without limitation or exception.