A dismissal would likely be by vote of the Senators.
I think it would be well within the authority of the Chief Justice to inquire of the Senate whether or not hearsay shall be accepted as evidence. This would shorten the proceedings considerably.
Along the same lines, I think he could inquire as to whether it shall be permissible to dismiss the charges against Trump for failure to state a specific impeachable offense. A vote by 51 Senators to allow such a dismissal would grant the Chief Justice that authority.
I don't think that the Chief Justice would be bound by what any single Senator decides. I am quite convinced the vote of 99 Senators to reject the impeachment would suffice to accomplish just that.