I did play in a police pipe band and they followed the Black Watch precedent of plain glengarries for pipers and red and white diced for drummers. I always thought the whole band should have had black and white diced glens, since police have black and white dicing on their hats (or is it navy and white?).
Depends on the police force. The City of London Police wear red and white dicing on their peaked caps, while other police forces in the UK use black and white. Blue and white police dicing is most commonly found in Australia and New Zealand.

Sir Percy Sillitoe, who was the Chief Constable of the City of Glasgow Police, is credited with the adoption of dicing for peaked caps in 1932. Sillitoe believed the dicing would make officers more visible in the evening. The pattern is known as "The Sillitoe Tartan", and is worn by several departments in Illinois and Pennsylvania.

T.