The feet of several of the cows were bound and some were missing part of their ears, the Swedish news agency TT reported.
The first cow was found in Gislov harbor on New Year's Eve. Carcasses of the other animals were on the shoreline as much as 56 miles away.
Police want to know if the cows were dead before they went into the water. Dumping slaughter waste in water is illegal. Depending on the circumstances of the cow's demise, the owner could be charged with animal cruelty.
"Our hypothesis at the moment is that the cows were dumped from a ship," said Jimmy Moden, a spokesman for the Skine police department. "But we can't say for sure how the ears were damaged, how they died, or if the cows are Swedish."
The ears may have been removed to avoid identification, particularly if the animal was sick, said police spokeswoman Ewa-Gun Westford.
The origin of the cows will be the focus of the investigation.
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