Synopsis As Introduced Amends House Rule 37. Provides that, while a Senate Bill is pending in the Senate, a House member may file with the Clerk a request to become the Principal Sponsor of the bill upon its arrival in the House, unless a previously submitted request remains pending. Authorizes a member to withdraw the member's request before arrival of the bill in the House. Specifies that, notwithstanding Rule 37(a), these sponsorship requests and withdraw of requests shall be noted in the Legislative Digest and on the General Assembly website.