Dependant T-SQL comparison collation
Along the lines of this with 2 where conditions.

One will be become '%string%' LIKE '%string%' which is always true

WHERE
    CASE WHEN @casesenstive = 1 THEN COL3 ELSE '%string%' END
           COLLATE SQL_Latin1_General_CP1_CS_AS LIKE '%string%'
    AND
    CASE WHEN @casesenstive = 0 THEN COL3 ELSE '%string%' END
           COLLATE SQL_Latin1_General_CP1_CI_AS LIKE '%string%'