They've also launched a GoFundMe site to play for repairing the vandalism.
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The mural, designed and painted by Garner artist Vincent Wood, was defaced by the words "Kill A Cop, Save A Child" scrawled in white on the building on 7th Avenue.
Chief Brandon Zuidema said they're taking the message seriously.
"I don't think we can do anything but assume it is a real threat. I think we'd be foolish to do anything else," he explained Monday.
The backdrop to the message is obviously the national debate over police involved shootings of young men - even children. But Garner's top cop says police relations here aren't that volatile and he reminded people that police have been targets too.
"They shouldn't have to worry about somebody doing something like this to put their lives in danger. They shouldn't have to worry like the cop in Texas did that was pumping gas and got shot. It's absolutely unacceptable and it's got to stop," said Zuidema.
Police say the vandal probably struck sometime Thursday night, and the damage was spotted Friday morning.
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Similar language was also found painted at a Garner shopping center.
Anyone with information is asked to call the Garner Police Department at (919) 772-8810.
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