Here is a paragraph from the web page of the
Colorado Public Defender's office:
"The Public Defender may find that it has a conflict of interest in representing you.
The most common reason for a conflict happens when you are accused of a crime along with other people and the Public Defender represents one of them. If this happens, the Public Defender can only represent one person who was charged. When this happens, the court will appoint you a lawyer from the Office of Alternate Defense Counsel (ADC). ADC contracts with private lawyers to provide court-appointed counsel.
Even if there is a conflict of interest, you still need to apply for court-appointed counsel through the Public Defender’s office. That office will advise the court of the conflict and the need to appoint an ADC lawyer."
Some have speculated here that Morphew had an accomplice for at least some part of the murder plan. There are other reasons the PD would need to conflict off a case, including what is called "conflict of commitment." But the bolded language above may well fuel speculation.