I am wondering if "the reader is referred to ..." sounds rude to a native ear.
If this sentence is kind of rude, then what else can I use as an alternative to it?
This is not rude, in my opinion, it's effectively a footnote in written text. It is somewhat formal and its spoken equivalent ("I would refer you to...") would not be common, but it would not be rude unless spoken aggressively.
Referring to "the reader" in the third person sounds very old-fashioned, very formal, and very academic, but it's not rude.
Academic writing tends to be very terse by nature, so it's difficult to be rude in that context. If you're writing for a particular academic journal, you should read in that journal for examples where other authors gave references of this kind and use the same phrases they use. For example, you could simply say,
For more information, see ...
or
see also ...
or simply use a footnote or endnote to provide the reference.