Is it my alternator or battery?

I have a 99 ford crown Vic police interceptor. This happened to me twice. One day I was driving and I was pulling into the auto zone to go buy oil. The second I turned into the parking lot my car cut off and the battery light came up on the dash board and it was really HARD to turn my car! Not even 2 week later my car did the same thing in McDonald's parking lot! Like it starts up with no problem so I don't know how it could be dead but it shuts off and making it hard to turn. I'm scared to drive it far places and not being able to turn properly and hitting someone. Help please. I read that it could be my Alternator or dead battery but my car starts fine.

Read more: Is it my alternator or battery?