In the United States we are fortunate that lurid allegations concerning Freemasonry and law enforcement are rare. In other countries, especially across Great Britain, press accounts are more common that attempt to link Freemasons with wrongdoing, and expecially if there is the slightest hint of any Masonic connection to the police or the judiciary. The British press is overly fond of making certain that a criminal's Masonic membership, if it exists, gets plastered in the opening paragraph of any story. And former Home Secretary Jack Straw's notorious witch hunt against Masons in law enforcement in the U.K. made headlines for years, even though it found zero evidence of any improper influence of Freemasonry on police or other justice officials.
Curiously, there does appear to be a visual connection between police and Freemasonry in the U.S. It's right out in plain sight, and has been for over a century. It is the official seal of the Fraternal Order of Police. At first glance, it's not obvious, but on closer inspection, the All Seeing Eye and a fraternal handshake can be seen in the bottom points of a five-pointed star.
Symbols are curious things, and any seal that is an amalgamation of symbols borrows liberally from other sources. The FOP explains theirs on their website:
The five-cornered star tends to remind us of the allegiance we owe to our Flag and is a symbol of the authority with which we are entrusted. It is an honor the people we serve bestow upon us. They place their confidence and trust in us; serve them proudly.
Midway between the points and center of the star is a blue field representative of the thin blue line protecting those we serve. The points are of gold, which indicates the position under which we are now serving. The background is white, the unstained color representing the purity with which we should serve. We shall not let anything corrupt be injected into our order. Therefore, our colors are blue, gold and white.
The open eye is the eye of vigilance ever looking for danger and protecting all those under its care while they sleep or while awake. The clasped hands denote friendship. The hand of friendship is always extended to those in need of our comfort.
The circle surrounding the star midway indicates our never ending efforts to promote the welfare and advancement of this order. Within the half circle over the centerpiece is our motto, "Jus, Fidus, Libertatum" which translated means "Law Is a Safeguard of Freedom."
Certainly the five-pointed star was an early Masonic symbol (seen more in Europe these days than in mainstream U.S. jurisdictions), as a symbol of the five points of man (head, hands and feet), as well as the five points of fellowship. It survives today in the U.S., albeit inverted, as the symbol of the Order of the Eastern Star. The All Seeing Eye is by no means a purely Masonic symbol, and appears in Renaissance art as a Christian symbol for God (along with the far older Egyptian "Eye of Horus"). And the fraternal handshake appears in Masonic, Odd Fellows, and many, many other fraternal groups' artwork throughout the 18th century.
In addition, the seal in the center of the star is the coat of arms of the city of Pittsburgh, where the FOP was originally founded. The supposedly Latin motto is somewhat tortured grammatically, and any first year Latin student would have had their knuckles busted by Sister Mary Discipline over it. The design came from one of the founders, Delbert Nagle, the FOP's first Grand president in 1917, and was drawn by H. J. Garvy.
Nagle believed the motto meant "Fairness. Justice. Equality." After 50 years, a committee was formed to get to the bottom of the grammar problem, and several Catholic priests were consulted (including Monsignor John J. Doyle, historian for the Archdiocese of Indianapolis). The committee came up with the slightly corrected version of "Law Is a Safeguard of Freedom," even though that's something of a stretch as well.
The FOP was at first formed in secrecy in Pittsburgh because police in that city were not allowed to unionize. The FOP was technically not organized as a union, but a fraternity. Once the city's mayor approved of the group, it came out into the open. Like so many other fraternal groups that arose during the Golden Age of Fraternalism, it adopted customs originated in Masonic and Odd Fellows lodges, terms like grand lodge, passwords and handshakes.
Nagle also developed a "secret" ritual for initiates in 1916, based on the symbolism and "mysteries" of the FOP emblem. It's entirely likely that the specific All Seeing Eye and handshake images on the original seal were simply made from printer's block elements from existing fraternal artwork, which would account for their close similarity to Masonic artwork from the 1800s.
For all you'd ever care to know about the formation and history of the FOP, see Fraternal Order of Police 1915—1976: A History by Justin E. Walsh, Ph.D. Turner Publishing Company, 2004.