Robert Zimmerman told WOFL-TV, Orlando, his son suffered serious injuries in a fight with Martin, 17, including a broken nose and cuts on the back of his head, The Orlando Sentinel reported.
Sanford police reports also describe Zimmerman as injured after the shooting Feb. 26, but a surveillance video aired by ABC News Wednesday shows no signs of injuries as the 28-year-old neighborhood watch volunteer arrived at the police station. No bruises or cuts were visible on his face or the back of his head, and his shirt didn't appear to have blood anywhere on it.
The initial police report said Zimmerman was bleeding from the back of the head and nose, and after medical attention it was decided he was OK to go to the Sanford, Fla., police station for questioning, ABC said.
Zimmerman's lawyer later said his client's nose was broken when he scuffled with Martin, 17, who was black.
Zimmerman, 28, claimed he shot the unarmed Martin in self-defense under Florida's so-called "Stand Your Ground" law.
Robert Zimmerman of Lake Mary said he and his family are afraid for their lives and are now in hiding. He said he was shocked by the hatred and anger the shooting has inspired.
"It's just amazing. Some people are being so hateful, and the people who are being so hateful know nothing about what happened," he told WOFL.
In the video an officer is seen looking at the back of Zimmerman's head. However, no abrasions or blood could be picked up by the surveillance footage.
Zimmerman did not check into the emergency room following police questioning, ABC News said.
Also apparently missing on the video were grass or grass stains on Zimmerman's jacket, which was noted in the police report.
Martin's family, along with prominent civil rights leaders and members of Congress, have said Zimmerman's story doesn't add up and demanded Zimmerman's arrest. Thousands of supporters have turned out at rallies across the country.
Celebrity Families of 2014 [PHOTOS]