Yes, your former employer can provide truthful information about the reason you resigned. However, if they provide false information to a third party that causes you damage, then you may have a defamation claim.
Kirk J. Angel is an experienced North Carolina licensed attorney who focuses his practice on employment law. Mr. Angel, who has focused on employment law for more than 15 years, represents clients throughout North Carolina and more information about him is available at www.theangellawfirm.com This response is for general informational purposes and does not constitute legal advice. Additionally, this response does not create an attorney client relationship. If you need legal advice, please contact a lawyer in your state who practices in the appropriate area.
I agree with Mr. Angel. Also note that the law treats a resignation in light of drug test as an admission that you knew you would fail. If you apply or have already applied for unemployment, you need to have a good explaination as to why you resigned if you hope to get benefits.