Photography in public places like public parks is not a crime. What is a crime is to be harrassed by other citizens and police when exercising your 1st amendment right to photograph in public places.
This is an article about what happened to a photographer in Sanford Florida and Lorton Virginia.
The 1st Circuit Federal Court of Appeals said that a lawyer who used his cell phone to record a video of police making a drug arrest was within his rights and that the seizure of his cell phone and his arrest by police violated his First and Fourth Amendment rights.
http://teejaw.com/tag/simon-glik/
In answer to the question, “Is there a constitutionally protected right to videotape police carrying out their duties in public?” the Court gives a resounding “Yes!”