That would depend entirely on what your obligation is under the Final Decree and/or any Marital Settlement Agreement and why you may need to go on Cobra. Normally, there is an obligation to continue coverage of a spouse's health insurance after a divorce under the Rhode Island Health Insurance Continuation Act. However, there are limits to this and normally the covered spouse must pay for any excess cost to for covering them. The general requirements of the law may be modified in the Final Decree or Marital Settlement Agreement so it is important to refer to those documents.
Please consult with an experienced Rhode Island divorce attorney to get a complete understanding of your rights and obligations.
Rhode Island is a very small jurisdiction so it's important that you consider the possibility that people who you know may see your question or that the facts discussed here may be subject to discovery requests if you become involved in litigation. Please remember that it is not possible to give proper legal advice without a thorough consultation and this answer is meant only to provide you with some guidance. Contact an experienced attorney at your earliest convenience to discuss your case thoroughly. The above was provided purely for informational purposes and does not create an attorney-client relationship between the questioner and the attorney.