Here is a study that attempted to link sleep deprivation to "false confessions." I don't have access to the entire study, only the summary article referenced above. Researchers studied 88 participants in a research lab, where some were sleep deprived for 24 hours and others slept 8 hours. The researchers had the participants take a series of computerized tests and were told not to press the 'Esc' key as that would delete data. At the end of the study, the participants were asked to sign a statement stating they had pressed the 'Esc' key. Results showed that 50% of the sleep-deprived people vs only 18% of the well-rested people signed the 'false confession.'
I'm not sure this demonstrates that sleep-deprivation leads to more false confessions. It may be that sleep-deprivation causes individuals to pay less attention to what they are reading. Signing something at the end of a research study has far less implications than signing a confession statement where you are being accused of a crime you didn't commit. In the latter instances, adrenaline may offset the affects of any sleep deprivation.