I got a PhD offer from a good university, and they told me that I should announce my final decision in less than four days. Many other universities have not started interviews yet, and I really want to consider all of my possible options. I do not want to lose this offer, too. The university is also part of the Resolution Regarding Graduate Scholars, Fellows, Trainees, and Assistants.
You have a trial period for the PhD, as in any job offer. Read the fine prints of the offer you received. The Resolution you mention states that:
If a student accepts an offer before April 15 and subsequently desires to withdraw that acceptance, the student may submit a written resignation of the appointment at any time through April 15. Applicants are not required to obtain a formal release from the program whose offer they accepted, either before or after the April 15 deadline. Once applicants have informed the program that they are withdrawing their acceptance of the offer, they then can accept any other offers
but there are many exception to the Resolution, so I strongly suggest you to contact the admission office of the University to ask if a Phd in (whatever subject is your offer) is covered by the Resolution.