The Massachusetts State Constabulary was formed in 1865, making it the oldest state law enforcement agency in the United States. Initially it was a small force charged only with investigations, and over the subsequent years it was renamed first the Massachusetts Detective Force and then the Massachusetts District Police. In 1921, it was reorganised, expanded and renamed the Massachusetts State Police Patrol, and its remit was expanded to patrolling rural areas of the state which were poorly served by the municipal police departments (Massachusetts, as previously stated, having no county police presence). Initially it had only fifty officers, but its strength probably increased considerably throughout the decade.
MSPP officers have the power to enforce state and federal laws throughout Massachusetts. Their primary mode of transport in the 1920s is still the horse (since many rural roads are still unsuitable for motor vehicles), but they increasingly also use motorcycles, particularly as patrolling major highways is added to their brief. Some cars are also acquired. Investigators could well encounter a motorcycle-borne MSPP officer while driving on the Aylesbury Pike.
The organisation of the MSPP in the 1920s is not easy to establish. A couple of histories of the agency have been written, but they are out of print and don't seem to be available in libraries outside Massachusetts. Some information can be gleaned from the MSP website, but it's not particularly good on history.
Covers the northeastern part of the state, including Essex County. Established in 1921.
Andover Barracks: The current colonial-style barracks was built in the late 1920s and opened by 1928, but there was probably a barracks in the Andover area before this, as it was designated A-1. Situated on Route 125, near the junction with Route 28, and responsible for policing both highways, as well as the local rural area. Still occupied by the MSP today.
Concord Barracks: Situated on Route 2 in West Concord and responsible for patrolling that, as well as the local area. Another barracks in identical colonial style to Andover, apparently built in the 1930s by the Works Progress Administration. Still occupied by the MSP. Just across the road from the Massachusetts State Reformatory and provided support to the warders there during prison riots.
Framingham Barracks: Troop A Headquarters. Situated at 450 Worcester Road (Route 9) and a typical early 1930s colonial-style building.
Topsfield Barracks: Situated on Route 1. Identical in appearance to other colonial-style barracks, so probably also opened in the late 1920s or early 1930s. Now used as the headquarters of Topsfield Police Department, having been replaced by the new MSP Barracks in Newbury in 1987. This barracks almost certainly covers the Lovecraft Country part of Essex County in the 1920s. Despite it being mentioned by Chaosium that the nearest State Police Barracks to Arkham is Danvers, the Danvers Barracks didn't actually open until 1994 to house a unit not established (at Lynnfield, later moving to Peabody) until 1956. The Topsfield Barracks are about 9 miles from Arkham, 12 miles from Kingsport, 6½ miles from Bolton, and 11½ miles from Innsmouth.
Covers the western part of the state. Established in 1921.
Cheshire Barracks: Established in the mid-1920s, but replaced by Pittsfield Barracks in 1937 (although it moved back to a brand-new building on Route 8 in Cheshire in 1987).
Lee Barracks: Troop B's first barracks, established in 1921. The present colonial-style barracks, situated on Route 20 (215 Laurel Street), were built in 1931 and are still used by the MSP. The original barracks was a barn in East Lee (also probably on Route 20), with the horses housed on the ground floor and the troopers in the loft.
Leeds Barracks: Troop B Headquarters. Situated in a converted barn and residence. It was replaced by a new colonial-style barracks in Northampton (555 King Street on Routes 5 and 10), still used by the MSP, in 1931.
Monson Barracks: Established in the early 1920s and issued with at least one patrol car. Replaced by Springfield Barracks in 1987. Probably situated on Route 32. See also the Hampden Police Department website.
Russell Barracks: Housed in a wooden building known as Fort Apache, about a mile to the west of the present barracks on Route 20 built in 1959.
Shelburne Falls Barracks: Another colonial-style building which looks to have been constructed in the 1930s. No hard evidence it existed in the 1920s. Situated at 289 Mohawk Trail (Route 2).
Covers the central area of the state. Presumably established in 1921 or 1922.
Brookfield Barracks: Another colonial-style building erected in 1930 on High Street and still used by the MSP. Situated on Route 9, the main road between Boston and New York.
Charlton Barracks: There is a current Charlton Barracks built in 1957 on the Massachusetts Turnpike, but it appears there may have been another which has now been replaced by the Sturbridge Barracks.
Grafton Barracks: A colonial-style building dating from 1931 at 44 Worcester Street (Route 140). Replaced by a new barracks in Millbury in 2006, it now houses the MSP Museum.
Holden Barracks: Troop C Headquarters. A colonial-style building at 612 Main Street (Route 122A) dating from 1930
Petersham Barracks: Moved to Westminster at some time in the 1920s or early 1930s, then to the present colonial-style building on Route 2 in Athol in 1934. This is the barracks that covers Winchendon, the site of the fictional Aylesbury, so could probably be replaced by Aylesbury Barracks in a Lovecraft Country setting.
Covers the southeastern area of the state. Established in 1922.
Middleboro Barracks: Troop D Headquarters. Replaced by a new building elsewhere in Middleboro in 1956.
Nantucket Barracks: Situated at 83 North Liberty Street and covers Nantucket Island.
North Dartmouth Barracks: Situated at 262 State Road (US Route 6). Replaced by a brand-new building in 2006, although the old building still exists
Norwell Barracks: A colonial-style building presumably dating from the early 1930s at 6 West Street.
Oak Bluffs Barracks: Situated on Temahigan Road and covers Martha's Vineyard and the Elizabeth Islands.
South Yarmouth Barracks: Another colonial-style building presumably dating from the early 1930s at 1171 State Road (Route 28).
West Bridgewater Barracks: Closed in 1956.
Photographs on the website of the Massachusetts State Police Museum show that the uniform in the 1920s and 1930s was surprisingly modern, with a peaked cap, riding breeches, knee boots, and a thigh-length leather coat for cold-weather wear. Since the photos are black-and-white, the uniform colours are difficult to determine (I believe the current "French and Electric Blue" of the MSP wasn't adopted until the 1930s). A 1931 Ford Model A Cruiser is shown on another page. It does appear to be in colours very close to the modern colours: mainly dark blue, with light blue (not quite the modern electric blue, but close) doors, roof and bonnet (hood) top, with "STATE POLICE" written down the sides of the bonnet and the MSP badge on the doors.
It seems reasonable to assume, given the force's small size in the 1920s, that each MSP barracks was staffed by only a handful of men (probably a sergeant and 3-4 troopers).