It depends if the child is subsequently adopted.
Under C.R.S. 19-5-104(5), after a relinquishment, the relinquishing parent or parents no longer have legal rights or obligations to the relinquished child. However, the relinquishing parents have a support obligation to the child. Likewise, a relinquished child's status as an "heir" does not cease at the time of relinquishment and the child may inherit from the relinquishing parents.
If the relinquished child is subsequently adopted, then the child does not have the right to inherit from the relinquishing parents. If you have questions regarding relinquishment, adoption, or inheritance, please contact The Harris Law Firm at 303 515 5000 or visit us at www.harrisfamilylaw.com