It is helpful to know why she won't sign, but I agree with the above answer for the most part. Your petition should be changed (amended) before you have her served. It would need to be amended anyway, since your first one said that "no service is necessary".
(1) Amend your petition for divorce and call it "First Amended Petition for Divorce"
(2) Pay to have her served (about $75)
At this point that 60-day clock will be ticking. If she does not file an answer on time, seek a default judgment. Note that if you default her and she figures it out within 90 days, she can almost definitely get a new trial. If she does file an answer, try to settle your case without trial.
You need to hire an attorney, especially if you have any children. If you don't have any children and you have not accumulated any community property, then you can probably get this done inexpensively.
You will have to serve her via a private process server or the constable. Also, once she has been served, you will have to file a First Amended Petition for Divorce and send that to her via certified mail so that she has notice of the items that you changed in the paperwork - and also that the Court knows you two will not be coming to an agreement for your property and child issues. I would also set this matter for a Temporary Orders hearing so that in the interim, there are orders that everyone must abide by until your Final Decree of Divorce is not entered with the Court.
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