Court-Appointed Guardian Accountability and Senior Protection Act This bill amends title XX (Block Grants to States for Social Services and Elder Justice) of the Social Security Act to direct the Department of Health and Human Services to award grants to the highest courts of states to conduct demonstration programs that: (1) assess adult guardianship and conservatorship proceedings, including the appointment and the monitoring of the performance of court-appointed guardians and conservators; and (2) implement changes deemed necessary as a result of the assessments, such as requiring background checks for all potential guardians and conservators, and establishing systems that enable electronic filing and review of the annual accountings and other required conservatorship and guardianship filings. The highest court of a state awarded such a grant shall collaborate with the state's own Unit on Aging and its Adult Protective Services agency in conducting the demonstration program.