The card, sent to the Eastern Daily Press in Norwich, shows a rough sketch of a motorcycle with stick drawings of a man and girl standing alongside. It carries the words 'Griston Road, Watton', the date 23 December and the time 9pm - about 45 minutes after the teenager was last seen at her home in Watton.
Norfolk police said scientists were examining the card for clues. This could include fingerprints and electrostatic document analysis to look for the impressions of writing on other documents which may have been on top of the card.
Police believe the killer of Johanna may be being shielded by a local person or family. Her body was dumped in a gravel pit in Watton likely to have been known only to locals. It was only accessible through dense brambles. 'We believe the killer must have damaged their clothing in some way dragging Johanna through the undergrowth,' police said. 'We want to know if anyone has bought themselves a new coat or anorak - or suddenly been seen without a familiar one.
'It is possible it was a smart coat or jacket of the type that would be worn when out for the evening. If it is no longer around, it is the kind of thing parents or relatives or friends would notice.'
Johanna, who went missing the day before Christmas Eve, was found in near-frozen water. Although she died from drowning, she had been beaten and her clothes partly removed. Police have not disclosed whether she was sexually assaulted or whether sufficient samples for a DNA fingerprint have been obtained.