Spoiler alert: It depends.
The short, easy answer is, yes, the First Amendment protects your right to film the actions of on-duty police officers, but the right is not without limits. The most common limitation on filming is when it interferes with police activities. As you probably guessed, the word interferes is subject to numerous interpretations. Also, at least right now, whether you have a First Amendment right to record the police depends on where you live. That is because as of July 2017, half of the federal appeals courts had formally recognized the right — the First, Third, Fifth, Seventh, Ninth, and Eleventh Circuits. The First Circuit includes most of the New England states; the Third is made up of Pennsylvania, New Jersey, and Delaware; the Fifth is Texas, Louisiana, and Mississippi; the Eleventh is remaining three southeastern most states (Florida, Georgia, and Alabama); the Seventh is Illinois, Indiana, and Wisconsin, and the Ninth Circuit includes the entire west coast, plus Idaho, Montana, Nevada, and Arizona. That leaves out most of the midwest, the mid-Atlantic region, and New York, Connecticut, and Vermont (see map of U.S. Circuit Courts of Appeals). The most recent decision was announced by the Third Circuit, in Fields v. City of Philadelphia, decided Jul. 7, 2017 by Judges Ambro, Restrepo, and Nygaard.
One evening in September 2013, Richard Fields, a sophomore at Temple University, was on a public sidewalk where he observed a number of police officers breaking up a house party across the street. The nearest officer was 15 feet away from him. Using his iPhone, he took a photograph of the scene. An officer noticed Fields taking the photo and asked him whether he liked taking pictures of grown men and ordered him to leave. Fields refused, so the officer arrested him, confiscated his phone, and charged him with ‘Obstructing Highway and Other Public Passages.’
But the Third Circuit didn’t get it all right. Despite holding that the First Amendment protects the right to film police activity, in the majority opinion, the court found that the right wasn’t “clearly established” at the time the Philadelphia police officers violated it. Under the doctrine of qualified immunity, government employees, such as police officers, are shielded from having to pay money damages to their victims unless the right they violated was clearly established at the time of the incident. Judge Nygaard disagreed with the majority, however, and in his dissenting opinion he cited the prior rulings of the other federal appeals courts, as well as the city’s own policy that protects the right of citizens to record the police. Fortunately for Richard Fields — the Temple University sophomore who was arrested for taking pictures of police breaking up a house party across the street — the Third Circuit remanded the case to the trial court on the issue of municipal liability, so it’s still possible that Fields could receive damages from the city.