Originally coming from the midwest, I'm well aware of America's perception of Central Park - "It's a crime waiting to happen"! But would you believe that this vast area has the lowest crime rate of the entire city reported annually by it's own Police Precinct which patrols the Park!?! So what about the terrifying headlines which make the National News...maybe once a year? These same acts of crime occur daily in other parts of the city you'll never know OR hear about. Yet, everyone knows and has heard of Central Park. Its headlines capture your attention...just as your safely being able to fully experience it will, too!
NYPD heavily and frequently patrols the park by car/motorcycle/cabbed scooters/bicycle/horse and on foot. You can't go far without seeing an officer to report any legitimate problem encounter you might have.
Common sense and confidence is all it takes to ensure a safe, memorable visit. Without these two, those who victimize easy prey will spot you a mile away which makes you no safer here than anywhere else in the city, or world for that matter. And for those who go looking for trouble, you'll likely easily find it, too!
Unless you've a specific destination already in mind, or interested in one of my activity suggestions, you'll probably have no need to venture far passed the 72nd St. area which brings you up to the Water Conservatory, Boat Pond and Strawberry Fields. These areas and south are heavily populated and traversed both day and night; usually there's additional safety in numbers. And yes, I said at night as a whole new brand of natural mystique and magic appears after dark worth checking out...only if you're confident.
At any time, your comfort level should determine how much of the 'off-the-beaten pathes' you explore through woods, bushes and lesser explored areas which can be pleasantly rewarding but can often conceal the sleeping homeless, drug dealers/users, pervs and other assorted sex mongers - all which also make the scattered public restroom facilities creepy. If that's what you're looking for, you'll surely find them...but otherwise potentially expect it and don't let it scare you off. Go about your business keeping comments to yourselves.
Police will tell you the majority of their daily duties involve assisting with a random purse snatching, lost child/people, vagrancy and lesser "Quality of Life" issues/infractions including urinating in public; especially when bathrooms are closed for the winter. Enforcing the Open Container law is definitely hit and miss so proceed accordingly and don't be surprised to see people drinking and to smell burning reefer everywhere.
FAST FACTS - The first Central Park murder happened in 1870 between a fueding Irish Catholic and Irish Protestant; the first mugging/murder happened to an "out-of-towner" in 1872.
The Park has a 1:00 a.m. curfew closing. Expect to be summoned if you're "caught" beyond this.
At any time of day, if randomly stopped by police, inability to produce a photo ID nets a guaranteed trip to the station.