I think the answer to this question very much depends on the rules and boundaries that are set up in your individual group relationship. If you don't have any, then I would suggest you discuss it with your partners first, and work out what would be considered the "right way" to do it for you.
Since my brand of poly tends to be more towards the polyfi end we have discussed this. Essentially, the prospective new person gets to meet the group before any sort of emotional investment is made. Since the expectation is that they will be a lot closer with the group, the intention is that everyone have a chance to get to know the person, and express their feelings about the person.
The dating process is also a little different in that it's not just the one person doing the "getting to know you" part, but that everyone takes part in at least the social aspect of the thing. For us, we really want to have a functioning friendship with the others, at the very least, so that has to be something with which everyone feels comfortable.
In a polyfi relationship, a mutual trust is even more vital so that has to be established.
"Listen, or your tongue will make you deaf." - Native American Proverb