According to inspector Shivram Vaingankar of Curchorem police station, the crosses were desecrated when policemen, who had been patrolling the area all through the night, left the spot this morning.
The crosses were located in Xelvona and Curchorem town areas, the police official told PTI.
A Hindu religious symbol and as many as five crosses were defiled in South Goa between July 1 and July 3 prompting Chief Minister Manohar Parrikar to hold a high-level meeting with police officials this week.
He had also asked police to engage all possible technologies including google mapping to track the accused.
Since then, police have been patrolling the religious places round the clock.
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