DEATH PENALTY: Is there a concept of self-incrimination for a capital crime in Biblical Law?
A: First of all, let me clarify to you that Biblical Law was applicable by the Bet haDin (a Jewish court) in a case involved capital punishment, a court of no less than 23 members, and it was applied only in the times when we had our Bet haMikdash and Bet Din haGadol, 2000 years ago. The Torah explicitly orders the application of death penalty for capital crimes such as intentional murder. Nevertheless, the legal requirements to actually execute the alleged criminal were highly complicated: For example, no circumstantial evidences were allowed. The only acceptable legal evidence was a direct testimony of two or more Kosher (which in itself was also part of arduous considerations) witnesses. And even when there were two Kosher witnesses, their testimony was explored and checked once and again and even if there was a minimal contradiction or incompatibility between the two witnesses, their testimony was disregarded.
As to your question, a confession was not accepted in a Jewish court. The rejection of self incrimination - in Hebrew: EN ADAM MESIM ET ATSMO RASHA - served also to eliminate the use of torture, which is very common in other cultures until today. The actual application of death penalty was exceptional. In a very famous passage, the Talmud expressed the improbability of execution, asserting that if a Bet Din put to death one prisoner during 70 years it was called a "murderer Bet Din." The strategy of the Bet Din was to dictate the death sentence in case the suspect was found guilty but virtually applying a kind of a life imprisonment by delaying indefinitely the actual application of the sentence.