Typically if you are the one backing up when a collision occurs you are the driver found to be responsible for damages sustained in the accident. If the police came and made a report of the accident, this may also help decide fault. Ultimately for claim purposes the insurance companies involved will investigate the accident claim, get statements from each driver and determine who they find at fault or if they find both drivers to be at fault.
In some states both drivers may be found to be partially negligence and thus both partly at fault. To find out who will be held responsible and found at fault for your specific accident, contact your insurance provider. For information on how to place an insurance claim you can read our article, Simple Steps to Filing Your Car Insurance Claim.