This character is a Nonspacing Mark and inherits its script property from the preceding character.
The glyph is not a composition. Its width in East Asian texts is determined by its context. It can be displayed wide or narrow. In bidirectional text it acts as Nonspacing Mark. When changing direction it is not mirrored. U+0324 prohibits a line break before it. The glyph can be confused with 4 other glyphs.
The Wikipedia has the following information about this codepoint:
Diacritical marks of two dots¨, placed side-by-side over or under a letter, are used in a number of languages for several different purposes. The most familiar to English-language speakers are the diaeresis and the umlaut, though there are numerous others. For example, in Albanian, ë represents a schwa. Such diacritics are also sometimes used for stylistic reasons (as in the family name Brontë or the band name Mötley Crüe).
In modern computer systems using Unicode, the two-dot diacritics are almost always encoded identically, having the same code point. For example, U+00E4äLATIN SMALL LETTER A WITH DIAERESIS represents both a-umlaut and a-diaeresis. Their appearance in print or on screen may vary between typefaces but rarely within the same typeface.