Electoral Count Reform and Presidential Transition Improvement Act of 2022 This bill revises the process of casting and counting electoral votes for presidential elections. The bill also revises provisions related to the presidential transition process. The bill specifies that the choice of electors must occur in accordance with the laws of the state enacted prior to election day. Additionally, the bill identifies each state's governor (unless otherwise identified in the laws or constitution of a state in effect on election day) as responsible for submitting the certificate of ascertainment identifying the state's electors. Further, the bill provides for expedited judicial review for any action brought by an aggrieved presidential or vice-presidential candidate arising under the U.S. Constitution or U.S. laws with respect to the issuance or transmission of such a certificate. The bill revises the framework for the joint session of Congress to count electoral votes and make a formal declaration of which candidates have been elected President and Vice President. Among other changes, the bill (1) specifies that the role of the Vice President during the joint session shall be ministerial in nature, and (2) raises the objection threshold in Congress to at least one-fifth of the duly chosen and sworn members of both the House of Representatives and the Senate. The bill also revises the presidential transition process, including to (1) allow more than one candidate to receive federal transition resources under certain circumstances, and (2) require additional reporting by the General Services Administration.