Hillary was found dead outside Mbombela on Tuesday, four days after she was last seen alive on April 29 with her adopted three-year-old daughter. The child was found unharmed.
Police in the province responded to criticism from her family that they had failed to pick up that she was shot.
EFF and family spokesperson Sinawo Tambo said the family only became aware of Hillary's shooting through a post mortem. He said the EFF and Gardee family were sceptical about whether police were capable of properly investigating Hillary's death.
Col Donald Mdhluli dismissed these claims, saying police conveyed this information to her family and that they were allowed to share it with friends and other family.
Mdhluli added that police were on top of the investigation and would not share their findings with the public, but with the family.
Support independent journalism by subscribing to the Sunday Times. Just R20 for the first month.
LISTEN | “I must not be the first one to catch them,” says Malema