Unfortunately....is the benefit and detriment of having an "at-will" employment relationship. It is not professional of course and you can of course pass this along if the ex-employee ever asked for a recommendation. Keep in mind the flip-side is that you could fire the person w/o any notice either and you kept your options open with the 3 month trial period w/o having an employment agreement put in place. Just make sure if the employee files for unemployment that you object based upon her voluntary resignation....and if you can coax her to give you a written resignation then you have the evidence needed to block an award for unemployment benefits.
My answer is not intended to be giving legal advice and this topic can be a complex area where the advice of a licensed attorney in your State should be obtained.
Yes, he is an at will employee. He can quit at any time; you can fire him at any time.
This answer is intended as informational only, and does not constitute legal advice or form an attorney-client relationship between us.
More and more employees do not give notice because more and more employers release employees once the employee gives notice.
If your business is one in which notice from departing employees is important to avoid disruption of operations, you should consider having employees sign a contract requiring the notice you need. However, you will need to also offer that same amount of notice if you terminate the employee (Ex: you need employees to give 30 days notice of resignation; you will have to give similar notice to employees or if terminated immediately, you will have to pay the equivalent salary of 30 days work).
The bottom line is you should be working with a qualified employment attorney. Nothing herein is meant to create an attorney-client relationship. Nothing herein is intended as legal advice.