The cut parts of the animal were allegedly noticed by the RSS volunteers who reached the park at Kishanganj railway colony to hold their 'shakha' this morning, according to local RSS leader Vagish Issar.
Police reached the spot and took into possession the animal parts for analysis.
A case has been registered and investigation has been taken up, said a senior police officer.
However, police were tight lipped about the incident, saying it was a "sensitive" matter and was being probed.
Cops from central and north districts were sent to the spot and the situation was "peaceful" although people were "apprehensive" of the incident, said the officer.
"The volunteers who reached the park for 'shakha' at 6 am found the cut pieces of cow there and informed the police. This is third such incident in past few months," said Issar.
The RSS volunteers said that recurrence of such incident in the area was feared by them to be an attempt to disturb communal harmony.
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