A 49-year-old man and a 44-year-old woman, from King's Lynn in Norfolk, were questioned by officers over the child's care and released on bail.
Police said intervention at this level was "very rare" and only occurred where other attempts to protect the child had been unsuccessful.
Almost one in three children in England is overweight or obese by age 11, so it is important to collect objective measurements of how children are growing.
Primary school children in Reception (age 4-5) and Year 6 (age 10-11) have their height and weight measured as part of the government's National Child Measurement Programme.
Parents in most areas will receive a letter with the results for their child, which will indicate if they are underweight, a healthy weight or overweight for their age and height.
This is judged by calculating their body mass index or BMI - their weight (in kg) divided by the square of their height (in metres).
The results are then plotted on a chart and collected by local public health teams.
A spokeswoman added police were working with health and social services.
The Sun reported the couple's 11-year-old son is 5ft 1in (1.5m) and 15 stone, with a body mass index (BMI) of 41.8.
It alleged concerned teachers and doctors prompted intervention by social services and then police.
Police and Norfolk County Council said it would not discuss the "victim" or the circumstances of the case.
'Protection from harm'
The couple were arrested in March on suspicion of child neglect and cruelty under section 1 of the Children's Act 1933.
"When dealing with sensitive issues such as obesity and neglect of children, officers from the force's Child Abuse Investigation Unit work closely with partners, significantly with both health care and social services, to ensure any response to address them are proportionate and necessary," police said.
"Any action taken by any agency will be subject to a joint strategy and will always be taken with the welfare of the child and their protection from harm as paramount."
Norfolk County Council spokeswoman said: "Our priority will always be the health, well-being and safety of Norfolk's children and we will always do all we can to support families to meet their children's needs."
In August 2012, a five-year-old girl from Newport, south Wales, was taken into care after her weight reached 10st 5lbs (66.1kg) - more than three times the weight of a healthy child her age.
http://www.bbc.co.uk/news/uk-england-suffolk-27730696Statistics: Posted by wendy — 06 Jun 2014, 16:13
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