"What time does your website close?" in Poole and "Can I exercise my kestrel on your tip?" in Nottingham are among the top ten bizarre calls of the last year.
Three of ten were made in Somerset, including: "What are the rules and regulations for hosting a mouse race?"
Councils are people's "first port of call" whatever the query, says the LGA.
The Local Government Association said councils' customer service hubs in England and Wales handled more than 50 million calls a year - the bulk of which are about council tax and parking.
But it compiled its top ten of the "slightly amusing to the outright bizarre" queries received in the past 12 months.
Peter Fleming, of the LGA, said: "These light-hearted examples of calls highlight the variety of issues that councils deal with every day."

Energy stocks also bounced back as the price of oil stabilised after falling sharply earlier in the day.
The Dow Jones Industrial Average climbed 55.47 points to 20,006.94 and the wider S&P 500 index rose 9.77 points to 2,399.29.
The Nasdaq index also increased, closing up 25.42 points at 6,100.76.
The US Department of Labour reported that US employers added 211,000 jobs in April, and the unemployment rate dropped slightly to 4.4% from 4.5% in March.
Some car companies and other retailers have been reporting weak sales figures.
However the jobs numbers were welcomed by the market as a sign that consumer spending, the mainstay of the American economy, is unlikely to diminish.
GDP growth also slowed in the first three month of 2017, but the period is often subject to data distortions.
The Federal Reserve said earlier this week it believed any slowdown was temporary.
"The Fed has made clear it is going to look through some of the weak economic data that's been coming through as they believe the fundamentals of the economy are strong. This number is something of a vindication of that view," said Luke Bartholomew at Aberdeen Asset Management.
But retail's troubles have not disappeared.
Shares in the cosmetics company Revlon plunged more than 23% on Friday after the company reported a loss in the first three months of 2017, driven by sales declines in North America.

Kerry Reeves died two days after being shot in Abingdon on 3 November.
Billy Johnson, 20, from Ripon Court, Corby, Northamptonshire, and Charles Noble, 20, from Kempton Avenue, Northolt, Ealing, have both been charged with her murder.
They appeared at Oxford Magistrates' Court and will next appear at Oxford Crown Court on Monday.
Ms Reeves, 26, was found in Thornhill Walk. She was taken to the John Radcliffe Hospital in a critical condition where she later died.
A post-mortem examination was carried out on Monday, where the preliminary cause of death was given as a gunshot wound to the head.
Questions on everything from James Bond villains to Great British Bake Off cake tins have been received by council call centres in England.
[NEXT_CONCEPT]
(Close): Wall Street markets closed the week on an upbeat note, after a strong US jobs report pointed to further economic growth ahead.
[NEXT_CONCEPT]
Two men have appeared in court charged with the murder of a woman who was shot in the head in Oxfordshire.