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Police received the vandalism report on Tuesday from the First Lutheran Church at 600 Homer Avenue.
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They say the flag was mounted to the outside of the church and was torn down sometime between May 7 and May 11 by an unknown suspect.
The flag was left on the ground and the wall was damaged.
Police say they do not have any information on the suspect yet.
Anyone with information can call the police dispatch center at (650) 329-2413 or email anonymous tips to paloalto@tipnow.org.