Gordon Brown unveiled a £30m fund in December's pre-Budget report to help voluntary and community groups assume ownership or management of assets such as unused community centres or playing fields.
But the announcement has reignited long-standing fears among some councils that far-right or extremist groups could gain control of assets and services.
The association says it strongly supports Brown's initiative, but that local authorities still have some concerns.
"We need to make sure that groups that are given the assets remain representative of the community as a whole and that it's something the community would want to happen," said a spokeswoman. "We will be looking for guidance about which kind of groups assets should be transferred to."
An official review of community ownership and management under Barry Quirk, chief executive of Lewisham Council, could lead to clarification.
"We understand these fears about unrepresentative groups," said Hugh Rolo, community enterprise manager at the Development Trusts Association.
"However, we believe there is a vital role for local participation and leadership. We hope that simple rules can be established that will not cause undue delay to the fund's implementation."
The Local Government Association has also voiced concern that groups that gain ownership of community assets might be free to sell them on for redevelopment - perhaps to supermarkets - in order to realise capital they could invest elsewhere.