Nope, it's optional for `style` tag too and defaults to `text/css`.

> The default value for the type attribute, which is used if the attribute is absent, is "text/css". 

[Ref 1](http://www.w3.org/html/wg/drafts/html/CR/document-metadata.html#the-style-element)

>  'text/css' is assumed if this attribute is absent.

[Ref 2](https://developer.mozilla.org/en-US/docs/Web/HTML/Element/style)