The relevant act is
local government finance act
which is here
http://www.legislation.gov.uk/ukpga/1992/14/schedule/3
i have only wasted three minutes wondering if the act says you have to pay the tax ( o god - does a sheep have five legs ? or does the pope have to be a roman catholic ?) ..... and in schedule 3 we find...
"Where a penalty is imposed on a person under paragraph 1 or 2 above, and he alleges that there is no power in the case concerned to impose a penalty of the amount imposed, he may appeal under sub-paragraph (1) or (2) above against the imposition.
4Where a person is convicted of an offence, the conduct by reason of which he is convicted shall not also allow a penalty to be imposed under paragraph 1 or 2 above."
and so on and so on
thre are other schedules with catching ambiguous headings like
Enforcement in Scotland ....
which fully answers to me the very vexed question
do we have to pay council tax ?
if your discussion was
is not paying council tax a crime like not paying the Poll tax was ?
I think the answer is no as you dont get a magistrates summons like you used to with Poll tax ( having had one ) if you dont pay council tax