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.
talk over
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Discuss thoroughly, as in Let's talk over the entire plan and see if we discover any flaws. [First half of 1700s]
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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
talk over
v.
1. To consider something thoroughly in conversation; discuss something: We talked the matter over. The panel talked over the proposal.
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To succeed in gaining the favor or support of someone by persuasion: We talked them over to our side.
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To speak and be heard amid some loud noise: It is impossible to talk over the noise of the machines.
Best Answer
When a person is the object of the preposition over, "talking over" is a type of interruption. The policeman was saying something, and the other person started talking before the policeman had finished all of what he was going to say.
Often when a person is interrupted, they will stop talking and let the other person go ahead and make their statement. However, the original speaker may not stop talking when the other person starts, expecting that the other person will quickly realize that they need to go back to listening and stop their interruption. When this does not happen, and both people end up speaking at the same time, the interrupter is said to be "talking over" the original person.
When someone is being persuaded, the phrasal-verb construction requires that the phrasal verb be 'split', with the object coming between the verb and the phrasal particle: "I talked him over". When someone is being interrupted, they will be placed after the preposition: "I talked over him".