The overwhelming majority of repeat cot deaths are from natural causes, a study says.
The researchers say screening could save lives
Researchers found eight in 10 sudden infant deaths in families who had already had a baby die unexpectedly were not suspicious.
The joint University of Sheffield and London School of Hygiene and Tropical Medicine team studied 6,373 babies.
Some 46 children died unexpectedly - 40 from natural causes and six from probable homicide, the report said.
Researchers said the findings, published in The Lancet medical journal, challenged suggestions that two or three unexpected deaths in the same family were more likely to be unnatural.
Report co-author Professor Robert Carpenter said: "Although child abuse is not uncommon, from the best available data, we believe that the occurrence of a second or third sudden unexpected death in infancy within a family, although relatively rare, is in most cases from natural causes."
Sudden infant deaths have fallen dramatically over the last 20 years from 1,700 a year in the mid 1980s to 175 in 2003.
Joyce Epstein, director of the Foundation for the Study of Infant Deaths, which funded the Care of the Next Infant programme on which the study was based, said it was an important piece of work.
"The study found that a second death is much more likely to be due to natural than unnatural causes.
"It shows that any form of automatic suspicion such as the so-called Meadow's Law is unjustified.
"This unique research shows how important it is to examine each infant death thoroughly and fairly and not leap to conclusions based on preconceived notions."
Meadow's Law refers to an observation in a book by the now-discredited paediatrician Professor Roy Meadow which stated: "One sudden infant death is a tragedy, two is suspicious and three is murder, unless proven otherwise."
Professor Meadow gave evidence in the case of Angela Cannings who was cleared on appeal a year ago of murdering her two baby sons.
Her case prompted the Attorney General to set up a review of sudden infant death convictions.
He has subsequently ordered the cases of 28 parents convicted of killing their children to be investigated further.