You are getting two errors:
Incorrect syntax near the keyword 'Case'.
and
Incorrect syntax near the keyword 'else'.
This should give you a clue that you are using the wrong construct. You actually want to use an IF-Statement - see
IF...ELSE (Transact-SQL) | Microsoft Docs[
^]. Something like
Declare @@ScriptRunDate datetime
set @@ScriptRunDate= DATEADD(mm, DATEDIFF(mm, 0, GETDATE()), 0)
select @@ScriptRunDate
IF @@ScriptRunDate
update Cssscript set ScriptState='Active' where id='Adhoc'
ELSE
update Cssscript set ScriptState='InActive' where id='Adhoc'
However the IF part is still wrong ... you probably want something like
IF @@ScriptRunDate = GETDATE()