Well yes and no.
In classic Chinese, there is no punctuation at all. I think the punctuation in Chinese are actually from European. All most all the punctuation you see in English are used in Chinese too. However because the way computer system encodes them differently, you see them differently on computer screen.
For example, the Chinese exclamation mark looks like these ！and English exclamation mark look like these !
In Chinese, single quotes are used when quoting a quote inside another quote. For example:
in this case, 我妈妈 is quoting 毛主席's 为人民服务.
Nevertheless, although in formal writing, you should always use the correct punctuation. In informal writing (for example, in txting, sms or chatting online), you can expect a lot of mix uses of both European punctuation and Chinese punctuation.