If a man does not have hair and therefore wears a toupee, may he wear the Tefillin Shel Rosh over his toupee? Can he fulfill the Misva in this fashion, or does the wig constitute a Hasisa – an "interruption" – between his head and the Tefillin, such that he is not considered as wearing Tefillin directly on his head?
The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) writes (27:16) that a wig indeed constitutes a Hasisa, and thus disqualifies the Misva. Both the straps and the box of the Tefillin Shel Rosh must be placed directly on the head, and therefore one who wears a toupee must first remove it before putting on the Tefillin Shel Rosh.
Rav Moshe Feinstein (Russia-New York, 1895-1986), in his Iggerot Moshe (Orah Haim, vol. 4, Siman 40), writes that if removing the toupee in public would cause a person embarrassment, then he may wear the Tefillin over the toupee in the synagogue, and without the toupee in private. Meaning, before going to the synagogue in the morning, he should remove the toupee, put on his Tefillin, and recite Shema. He should then remove the Tefillin, wear the toupee, and go to the synagogue, where he may then put on his Tefillin Shel Yad as usual, with a Beracha, and then put on the Tefillin Shel Rosh over the toupee "for show," not to fulfill the Misva. This ruling is codified by Hacham David Yosef in his Halacha Berura (vol. 2, p. 106; listen to audio recording for precise citation).
Rav Moshe adds that if a person undergoes a hair transplant, or has a permanent toupee that cannot be removed, then he may wear Tefillin normally over the implanted hair or toupee. Since it is placed permanently on the head, it is considered part of the head and does not constitute a Hasisa.
A more common issue concerning Hasisa with the Tefillin Shel Rosh involves gels or talc that some men use in their hair. The Hid"a (Rav Haim Yosef David Azulai, 1724-1806) and other authorities note that these kinds of substances that leave a film of powder or gel on the hair constitute a Hasisa between the Tefillin and the head. As such, men who use powders or gels must apply them only after praying in the morning with Tefillin, so that they can properly fulfill the Misva.
Summary: The Tefillin Shel Rosh must be directly on the head, with nothing in between. Therefore, a man who wears a toupee must remove it before wearing Tefillin. If he wishes, he may wear Tefillin without the toupee in private, to fulfill the Misva, and then in the synagogue wear it over the toupee. One may wear Tefillin over implanted hair or a permanent toupee. Men who use gels or powders in their hair must ensure not to apply them until after wearing Tefillin in the morning.