Did a particular town or suburb have a police force at one time?
Not all Scottish towns had separate police forces. Here is a list of those which did (with their dates of operation and the force which succeeded them). If the town concerned is not on this list it almost certainly did not have a separate police force, and was most likely served by the relevant county constabulary.
Aberdeen 1818-1975, successor force: Grampian.
Airdrie 1821-1967. Successor force: Lanark County.
Alloa 1822-1930. Successor force: Clackmannan County.
Anderston 1824-1846. Successor force: Glasgow City.
Annan 1858?-1881. Successor force: Dumfries County.
Arbroath 1836-1949. Successor force: Angus County.
Ardrossan 1859- ? Successor force: Ayr County.
Ayr 1845-1968. Successor force: Ayrshire.
Banff 1859-1886. Successor force: Banffshire.
Blairgowrie 1857-1875. Successor force: Perthshire.
Brechin 1859-1930. Successor force: Angus.
Broughty Ferry 1888-1913. Successor force: Dundee City.
Burntisland 1859-1861. Successor force: Fife.
Calton 1819-1846. Successor force: Glasgow City.
Campbeltown 1858-1863. Successor force: Argyllshire.
Coatbridge 1886-1867. Successor force: Lanarkshire.
Cromarty 1859-1868. Successor force: Cromarty County.
Cullen 1840-c.1861. Successor force: Elginshire.
Cupar 1859-1864. Successor force: Fife.
Dingwall 1859-1865. Successor force: Ross-shire.
Dumbarton 1855-1949. Successor force: Dunbartonshire.
Dumfries 1811-1932. Successor force: Dumfries-shire.
Dunbar 1844-1869. Successor force: East Lothian.
Dundee 1824-1975. Successor force: Tayside.
Dunfermline 1811-1949. Successor force: Fife.
Dysart 1858-1859? Successor force: Fife.
Edinburgh 1805-1975. Successor force: Lothian and Borders.
Elgin 1850-1893. Successor force: Morayshire.
Forfar 1857-1930. Successor force: Angus.
Forres c.1859-1867. Successor force: Morayshire.
Fraserburgh 1859-1866. Successor force: Aberdeenshire.
Galashiels 1850-1930. Successor force: Selkirkshire.
Gorbals 1808-1846. Successor force: Glasgow City.
Govan 1864-1912. Successor force: Glasgow.
Glasgow 1800-1975. Successor force: Strathclyde.
Greenock 1801-1967. Successor force: Renfrew and Bute.
Greenock Harbour 1817-1822, 1825-1843. Successor force: Greenock Burgh.
Haddington before 1857-1874. Successor force: East Lothian.
Hamilton 1855-1949, 1958-67. Successor force: Lanarkshire.
Hawick 1840-1930. Successor force: Roxburghshire.
Helensburgh 1846-1875. Successor force: Dunbartonshire.
Inverkeithing c.1859-1885. Successor force: Fife.
Inverness 1847-1968. Successor force: Inverness-shire.
Jedburgh 1857-1861. Successor force: Roxburghshire.
Johnstone 1857-1930. Successor force: Renfrewshire.
Kelso Burgh ?-1881. Successor force: Roxburghshire.
Kilmarnock 1846-1968. Successor force: Ayrshire.
Kilsyth 1840-? Successor force: Stirlingshire?
Kinning Park 1892-1905. Successor force: Glasgow City.
Kirkcaldy 1877-1949. Successor force: Fife.
Kirkintilloch 1838-1872. Successor force: Dunbartonshire.
Kirriemuir 1859-1891. Successor force: Forfarshire.
Leith 1859-1920. Successor force: Edinburgh City.
Lerwick 1892-1940. Successor force: Zetland.
Macduff 1859-1870. Successor force: Banffshire.
Maryhill 1856-1891. Successor force: Glasgow City.
Maxwelltown 1863-1890. Successor force: Kirkcudbrightshire.
Maybole 1859-1861. Successor force: Ayrshire.
Millport ? – ? Successor force: Bute?
Montrose 1833-1930. Successor force: Angus.
Motherwell & Wishaw 1930-1967. Successor force: Lanarkshire.
Musselburgh 1835-1841. Successor force: East Lothian.
Nairn 1859-1866. Successor force: Nairnshire.
Newburgh 1859-1969. Successor force: Fife.
North Berwick ? – 1857/8. Successor force: East Lothian.
Paisley 1806-1969. Successor force: Renfrew and Bute.
Partick 1858-1912. Successor force: Glasgow City.
Perth 1811-1964. Successor force: Perth and Kinross.
Port Glasgow 1857-1895. Successor force: Renfrewshire.
Pulteneytown 1858-1902. Successor force: Caithness-shire.
Renfrew 1857-1930. Successor force: Renfrewshire.
Rothesay 1846-1923. Successor force: Bute.
St Andrews 1858-1859? Successor force: Fife.
Stirling 1857-1938. Successor force: Stirlingshire.
Stranraer 1857-1870. Successor force: Wigtownshire.
Thurso 1841-1873. Successor force: Caithness-shire.
Wick Burgh Formed 1841-1858. Successor force Caithness-shire. Re-formed 1863-1873. Successor force Caithness-shire.
Wishaw ?- 1859. Successor force Lanarkshire.