Since i am using CSS to select the font, the charset should be the same, right?
Not necessarily: The font might not be installed on every machine, and fonts can have different versions. You can't trust every client machine 100% to have exactly the font you need.
See this question for more background and approaches to determine font support for a specific glyph: Unicode support in Web standard fonts
The only way to make pretty sure the user has the correct font is to embed it into your web page using @font-face or using a hosted one by Google Web Fonts. In all browsers that support this method, you can then trust the same font to be delivered to every client.
However, embedding a font using font-face
is tantamount to redistributing it, which most commercial licenses do not allow (see e.g. the Microsoft Typography FAQ). You would need to find a completely free font that allows redistribution this way - ideally one from Google's portfolio, or from a place like the Open Font Library.