Problem is that your String has a single quote characters which breaks your SQL Query String.
Simulating parametro == test01 - OK
"SELECT titolo, icona, colore, tipo, identificativo, dato_campo FROM table WHERE titolo LIKE '%test01%' OR dato_campo LIKE '%test01%' GROUP BY identificativo";
Simulating parametro == stringa' NOK
"SELECT titolo, icona, colore, tipo, identificativo, dato_campo FROM table WHERE titolo LIKE '%stringa'%' OR dato_campo LIKE '%stringa'%' GROUP BY identificativo";
As you can see, your string is producing '%stringa'%' which is invalid for a SQL query.
You should escape that character ' during your query to something like: %stringa''%'.
So, you can add something as follows before creating your Query String:
parametro = parametro.replaceAll("\'","''");
String sql = "SELECT titolo, icona, colore, tipo, identificativo, dato_campo FROM table " +
"WHERE titolo LIKE '%" + parametro + "%' " +
"OR dato_campo LIKE '%" + parametro + "%' GROUP BY identificativo";
This is a support about the issue that your are facing now... As Gabe Sechan mentioned on the other answer, raw queries should be discouraged.
UPDATE
Safe way to run your query is:
String paramentro = "stringa'";
Cursor cursor = db.query("tablename", new String [] {"titolo", "icona", "colore", "tipo", "identificativo", "dato_campo"}, "titolo LIKE ? OR dato_campo LIKE ?", new String[]{"%"+paramentro+"%", "%"+paramentro+"%"}, "identificativo", null, null, null);