section 494 ipc

Yes the Muslim woman can complaint under section 494 IPC against her Muslim husband on the following conditions only:

1. The Muslim husband married and registered the marriage with the Muslim woman under the Special Marriage Act,1954. After this first marriage, he goes ahead and marry another Muslim woman according to Muslim form of marriage.

2. The Muslim man already has 4  living Muslim wives married them according to Muslim form of marriage and goes ahead and get married to fifth woman according to Muslim form of marriage.

The muslim wife is not married in Special Marriage Act, 1954 and the husband is not having 4 Living wives. In such case whether complaint can be registered b'caz as per Constitutional law which prevails over Personal Laws ?

Constitution also provides freedom of conscience and free profession, practise and propagation of religion under Article 25. For Muslims in India having more than one wife (upto 4 maximun) at the same time is permitted according to the Muslim Shariat law that cannot be overruled by the Constitutional law that prevents bigamy or polygany for other Indian citizens in India.

Even if the private criminal complaint registered u/s 494 IPC by the first Muslim wife against the Muslim husband for indulging in bigamy, the Muslim husband will have the defence as mentioned above against the complaint and he will get discharged on this very ground.