Violence at the Star casino in Sydney increased after the city’s lockout laws were introduced but the number of extra assaults recorded was “not very substantial”, the New South Wales crime statistics agency has found.

The NSW Bureau of Crime Statistics and Research (Bocsar) said in a report on Tuesday there were about two additional assaults at the casino each month after the lockout rules were launched in February 2014. However, there were 13 fewer assaults per month in Kings Cross during the same period and 30 fewer in the CBD.

The casino was granted an exemption to the laws, which prohibit large venues within a precinct stretching from Surry Hills to The Rocks, and from Kings Cross to Cockle Bay, from allowing entry after 1.30am.

Drinks must also stop being served after 3am and new liquor licences have been suspended across the CBD and Kings Cross.

The laws were introduced after a spate of deaths at nightspots around Kings Cross, and they were praised at the time by Sydney’s main newspapers.

Bocsar examined police assault figures in the period between January 2009 and December 2015.

A similar report in June pointed to an increase in assaults in Pyrmont after the start of the lockouts. The assaults decreased in Potts Point and Darlinghurst but their number was largely static in The Rocks, Haymarket, Woolloomooloo, Newtown, Glebe, Paddington, Bondi, Waverley and Petersham.

The laws have stirred controversy in Sydney because of the alleged impact on nightclubs and nightlife in the city, and many believe they were unnecessary because the assaults were declining.

Thousands protested in the city in February against the laws, which have won favour among many doctors, nurses, emergency workers and police, but have been bitterly opposed by the music and hospitality industry.

The city’s lord mayor, Clover Moore, said in a submission to a review of the lockouts that they were a “sledgehammer” to Sydney’s nighttime economy and had failed to address “the real problems” with alcohol-fuelled violence in the city.

The review, by the former high court justice Ian Callinan, is expected to deliver its findings in August.