Assessing a woman's interest level on LinkedIn is pretty easy and low risk. Send her an invitation, if she accepts, then you can send a brief, i.e. 1 sentence text about something, anything. If she responds, you can proceed chatting, if not then drop it. No biggie, no damage to career. If you two keep chatting, there could be interest. Propose a lunch for networking purposes and assess her body language during the lunch. Do not be very aggressive as it's a networking lunch. Assess her reaction and act accordingly.
I ended up with a good female friend through LinkedIn once, someone I distantly knew at a company I used to work at.
Also, once, I happened to look at someone's photo on linked in, she then looked me up on LinkedIn. Then she send me an invite, which showed interest. We chatted and met in person. This woman turned out to be absolutely crazy. Very sweet, but nuts.
In my opinion, trying to hook up with someone on LinkedIn works best when it's with someone you kind of a knew at a job, couldn't get close to, i.e. knew of each other, and now the 2 of you work for separate companies and will probably never meet again work wise.