In an interview with the BBC, Ms Meynell said the force had referred itself to the Independent Office for Police Conduct (IOPC) over its handling of disciplinary procedures.
Barnaby Webber, Grace O’Malley-Kumar and Ian Coates were killed on 13 June.
Nottinghamshire Police’s Kate Meynell said a special constable had been sacked for viewing the bodycam footage.
Another staff member is set to face misconduct proceedings, with eight others who had “low-level access” receiving “standards interventions”.
Two police officers were also disciplined over a WhatsApp message, described as “crude and distasteful”.
The force is already being investigated by the IOPC, along with Leicestershire Police, following the case, which saw Calocane given a hospital order after admitting manslaughter on the grounds of diminished responsibility.
Ms Meynell said: “This is one of the most brutal and horrific incidents we’ve seen here in Nottingham, in our history.
“There’s lots of things I can’t say. And that’s not because I don’t want to, it’s because there’s the ongoing reviews into what happened.
“There is another case coming up. This relates to the police staff member who we know has access to systems around the offender in this incident. This is ongoing, so I can’t say much else. But there is no sharing of images… in relation to this individual.”
She called the actions of the special constable, who viewed bodycam footage of officers and paramedics providing assistance to Mr Webber and Ms O’Malley-Kumar, “totally unacceptable”.
“I’m not going to try and pretend that I feel the same horror as the families,” Ms Meynell said. “But as chief constable, I do feel horror that some members of my staff have behaved in that way.
“That is why we have dealt with them swiftly.”
