TL;D/R: Psychopathic criminals are no more intelligent than non-psychopathic criminals, but the highly intelligent ones are more likely to commit serious crimes.
The connection between psychopathy and intelligence is slight complicated. There were conflicting reports about whether psychopaths were more intelligent, or the same intelligence, as other criminals. [Note: They were compared to non-psychopathic criminals, not the general population which is what the question was about; I hope this is close enough.]
A Swedish study tried to tease out some of the complexity.
In the abstract, they explain the conflict:
Empirical studies using the PCL-R (Hare, 2003) have shown no intelligence differences between psychopaths and nonpsychopaths. However, Cleckley (1976) argued that psychopaths often show superior intelligence.
The study explored whether:
the correlation between intelligence and severity of criminal development is the opposite in psychopaths than in nonpsychopathic criminals using a sample of 370 men sentenced for violent (nonsexual) crimes. That pattern would provide a way of explaining the discrepancy between Cleckley's view and later empirical work.
for nonpsychopaths, higher total IQ and particularly verbal intelligence meant a later start in violent crime. For those diagnosed as psychopaths, however, this association was reversed.
The paper was further written up in Crime Times where they had more quotes from the authors.
"The key finding in this study is that psychopathic and non-psychopathic criminals, although not different in overall levels of intelligence, did differ in how high intelligence was related to the seriousness of misbehavior. For non-psychopaths, higher intelligence, particularly verbal intelligence, meant a later start in violent crime. For those diagnosed as psychopaths, however, high intelligence meant an early start in violent offending and more problematic behavior in and outside of institutions."