The ordinary Japanese word for 'skin' is hada, written in Chinese characters 肌 . There is a somewhat more formal Chinese compound with the same meaning, hifu, written 皮膚. It is the formal term hifu that is used to refer to a dermatological clinic or hifu-ka (皮膚科). This can be found in public signs for dermatological clinics, such as that shown below.
However, it is extraordinarily common to see the second character written in katakana (皮フ) as in the sign below:
This abbreviation is also very commonly found on the Internet, as a Google search will quickly reveal. Although somewhat less common, the hiragana version 皮ふ is also found.
As the character 膚 is found in the list of Chinese characters for ordinary use (the Jōyō Kanji), the only justification for adopting katakana here is the relative complexity of the correct Chinese character.
A Google search in August 2003 revealed the following distribution:
Notable is the relatively high prevalence of 皮フ科 as a way of writing hifu-ka (dermatological clinic).