The seven-month-old died at a house on Melrosegate, York, on 3 November.
The death prompted a Sheffield-based bed company to issue a product warning. A joint investigation between police and Trading Standards is under way.
North Yorkshire Police said the 35-year-old man from Rotherham, South Yorkshire, was assisting with the inquiry.
No cause of death for the infant has been confirmed.
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Police have issued a safety warning to customers of Playtime Beds Ltd.
"If they have ever had any safety concerns or a child has suffered an injury as a result of the design of the bed, then please contact us," a spokesman said.
Playtime Beds Ltd of Sheffield, which has ceased trading, is working with Trading Standards over safety concerns about products it had produced since 2011.
It issued a product warning in December which advised that risks to children could include asphyxiation or strangulation, falling, entrapment or crushing.
The company produced a range of bespoke children's cots, twin beds, bunk beds, cabin beds, high sleeper beds and triple and quadruple beds.
It added parents should stop using the beds immediately and to contact Trading Standards.
A man has been interviewed under caution by police investigating the sudden death of a baby.