I saw this video where two policemen, in three different times tell citizens "Don't talk over me" (0:12) or "you are talking over me" (3:37 also 3:44). It seems that all of these mentions in the video are with the same meaning. Anyway I don't know what it means but based on the context, I can guess that the meaning is "don't talk to me in a way that you are over me or better than me". Isn't it?
I searched for the meaning on this online dictionary and I'm not sure which one of the definitions matches this context, if any.
Discuss thoroughly, as in Let's talk over the entire plan and see if we discover any flaws. [First half of 1700s]
Win someone over by persuasion, as in We talked them over to our point of view. [First half of 1800s] Also see talk around. See also: talk
v. 1. To consider something thoroughly in conversation; discuss something: We talked the matter over. The panel talked over the proposal.
To succeed in gaining the favor or support of someone by persuasion: We talked them over to our side.
To speak and be heard amid some loud noise: It is impossible to talk over the noise of the machines.