The legislation, proposed by the Scottish Government, places a duty on councils to support people who voluntarily look after vulnerable relatives and friends.
It is backed by Carers Scotland, which says those providing such assistance face a postcode lottery, with some receiving help and respite from their local authority and others coping alone until they reach crisis point.
However, the Convention of Scottish Local Authorities (Cosla), which represents councils, believes the law is will result in money being spent on form-filling instead of help.
At the moment carers are eligible for an assessment if the care they provide is judged to be "regular and substantial".
In their response to the consultation on the law change, Cosla says: "The proposal to mandate that a formal assessment is undertaken for all carers, irrespective of the level of need, runs counter to the requirement to effectively target resources towards need. This carries the risk that councils are forced to invest scarce resources inappropriately."
There are estimated to be 660,000 carers living in Scotland. Councillor Peter Johnston, Cosla's health and social care spokesman, said: "By introducing a duty to support carers and applying eligibility criteria, councils will be forced to make a false dichotomy - automatically creating 'winners' and 'losers' - and tying up significant resource in the bureaucracy required to make and administer those distinctions. Not only does this divert resource towards bureaucracy at a time when we need every penny to go on care and support, it will make it harder for councils to take an holistic approach which looks at the carer's support needs within the context of the family unit, and indeed wider community, overall."
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Fiona Collie, policy and public affairs officer for Carers Scotland, said the test of providing "regular and substantial" care was interpreted differently by different councils.
She said she understood Cosla's concern about resources but added: "In one area carers may be getting good support, in another someone in almost exactly the same situation is in crisis because they are not getting support."
Cosla has told the Scottish Government that if the law is passed, it must provide extra cash to cover the "significant financial burden" it will place on councils.
A Scottish Government spokeswoman said it was "committed to ensuring that both carers and young carers get the support they need" and wanted to "accelerate the pace of change".
She added that the recent consultation on carers' legislation had received a positive response from many groups. "We will of course consider Cosla's views together with the views and comments from all other respondents," he added.