In short: no.
At the moment, you cannot post a message to your circles and to a community (public or private) at the same time. There are some legitimate concerns that if you do so you're exposing the community (or comments from members in the community) to people who are not in the community, and may not even be aware of its existence. While this may be ok for some private communities, it is probably not what most expect, which is a truly private place to talk.
Combining the two is a very tricky thing to navigate when it comes to private communities, and I don't expect them to address this issue further. But if you want to provide your input, and provide specific use cases where you think it makes sense and how you would like the privacy issues handled, make sure you use the Send feedback feature available under the gear icon.