A joint petition by definition is a settlement. A standard joint petition will have both parties waive the right to notice of entry of the Decree, among other waivers. If you use the forms from the Family Court Self Help Center, that language is included.
So, you will generally not have to "serve" the other side with anything.
If there is a litigated divorce you need to have the other party properly served. If it's being done on consent then signed documents will suffice.
Under the rules governing the conduct of attorneys in New York it may be necessary to remind you that this answer could be considered attorney advertising.
There is no service of process with a joint petition. You both have to sign, and then file all the necessary papers with the court to be processed. These "do it yourself" projects have a high failure rate in the court system. It is worth consulting with an attorney to make sure you are doing it right.
Responses are for general information purposes only, and are based on the extremely limited facts given. A consultation with an attorney experienced in the area of law(s) indicated in the question is highly recommended. Information and advice given here should not be relied upon for any final action or decision, as the information is limited by its nature to the question asked and the fact(s) presented in that question. THIS RESPONSE DOES NOT CREATE AN ATTORNEY/CLIENT RELATIONSHIP, particularly considering that the names of the parties are unknown.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.