After the last point was contested, Hamlet takes the question directly to Laertes first. He could have continued to ask for judgement from the outside authority but he goes to Laertes first. It’s a nice move, really. Or at least interpersonally sharp. Better to get the point from Laertes himself – keep the fight between them, rather than the outside authorities.
Ultimately none of it REALLY matters – they’re all gong to to die in a few moments – but at least – if, in death, we have to watch our last moments over and over, Hamlet won’t have to do a lot of wincing about his behavior.