The "Postal Service Clusterbox Responsibility Act" amends title 39 of the United States Code to mandate that the United States Postal Service (USPS) maintain specific cluster box units. This includes responsibilities such as repairing, replacing, and adding mailboxes to these units. A cluster box unit qualifies as a "covered cluster box unit" if it is privately owned and the USPS has primarily maintained it for a period of not less than 20 years. A covered person can apply to the USPS for a determination, providing documentation of historical maintenance and written permission for the USPS to continue maintenance. The USPS must investigate and make a determination within one month of receiving an application. For covered units, the USPS is required to add mailboxes if deemed necessary after a notice from a covered person, and will also maintain mailboxes added by others in accordance with laws and regulations. However, the USPS's maintenance obligations are limited; they do not cover repairs for intentional damage, changes not necessary for function, or structural building repairs. If maintenance costs arise from a third party's legal liability, the USPS may seek reimbursement or assignment of rights from the beneficiary. A cluster box unit ceases to be covered if permission for maintenance is withdrawn, a beneficiary refuses a reimbursement request, or the USPS permanently stops mail delivery to all addresses served by the unit. The bill also establishes a Cluster Box Unit Maintenance Fund in the Treasury to fund these activities. Finally, the Act requires the USPS to issue regulations to implement these amendments within 180 days of its enactment.