Well, I should have said many cops don't take radios home. Most departments keep radios and extra batteries charging at the station. But it's also common practice in some departments for cops to wear full uniform and be ready to respond in emergency on their way to and from work. This would include carrying a handheld radio, I assume. And some departments issue their officers patrol cars to take home with them so they can be on-call and ready to respond from home, so those folks are definitely going home with at least a radio in their unit, if not a handheld as well.
But some departments are the exact opposite and it's against regulations to have any uniform or work gear visible in your personal vehicle. I'm sure it depends on the kind of area you patrol. If you live and work in a small town and everyone knows you are a cop, why hide it on the way to work. I'd rather be in full uniform with all my equipment from the moment I step out of my home. But in a big city it would be much easier to get lost, especially if you commute a distance from your home to where you patrol.
I don't know what the Dallas PD does, but this officer being in uniform, probably not having a radio and using her cell to call 911 doesn't mean much one way or the other.