Smoking cannabis could mean a slightly increased risk
The study, published in the Journal of the American Medical Association, found the link between sudden infant death and fathers who smoked cannabis either around the time of conception, during pregnancy, or after the birth.
Smoking cannabis around the time of conception or during their partner's pregnancy doubled the risk of cot death.
If cannabis use was extended beyond the birth of the baby, the risk was almost trebled.
However, the authors of the study, from the University of California, say that this is not a definitive finding, calling for more research into the subject.
They looked at the cases of 239 infants who died from sudden infant death in their state between 1989 and 1992.
Mothers off the hook
Perhaps surprisingly in the light of their findings about fathers, maternal recreational drug use during pregnancy was not associated with an increased risk of cot death.
Dr Hilary Klonoff-Cohen, who co-authored the report, said that this might be either because women were less likely to admit smoking cannabis, or that men smoke more cannabis, more often.
The overall incidence of cot death is relatively low - approximately one in every 2,000 births in the UK.
Campaigns to encourage safe sleeping positions for babies have been credited with cutting the number of cases substantially during the 1990s.
The major risk factors appear to maternal smoking, which can increase the risk of cot death fifteen-fold.
Dr Ed Mitchell, from Auckland University in New Zealand, told New Scientist magazine that the risks posed by drugs appear slight in comparison.
He said: "I would emphasise that the major problem is maternal tobacco smoking when pregnant, rather than these other drugs."