Yes, there are referral schemes. If you know someone there, and assuming you don't know very well enough personally, the tactful way to approach this is to seek their thoughts in the first instance. Raise the fact you are thinking of applying to the firm and just ask for their advice openly - people like to have their opinions heard. You can ask whether they think you are suitable material for the firm, and assuming they give you a positive response ask whether the firm operates a recommendations scheme. If they are politely uncommital about your chances then leave it. Like any business relationship, don't be afraid to be assertive. However, as recommendations overlap with the personal relationship between recommender and recommendee, so you don't want to be pushy. The ideal situation is to have, or build, a relationship where the recommender actively wants to help you, feels that they can be honest without hurting your feelings, and gives you active feedback and feeds you information to maximise your chances of success at interview. You don't want them making a recommendation just because they feel obliged. From recent experience, the worst opening lines when a colleague brings you a recommendation are "My mate keeps bugging me to give you their CV" and "I have a CV knocking around in my bag that some girl asked me to pass to someone in your department - can I give it you?"
It can help get your foot in the door, although simply emailing your CV isn't likely to help as people will only recommend candidates who a) meet all the regular recruitment standards and b) who they trust not to show them up.
Although the reward for a successful recommendation is attractive, the more unsuccessful recommendations you make, the less your opinion and recommendation is valued by the hiring managers. Therefore there is a pretty strong incentive to only make strong recommendations.
I can't imagine the situation is much different even at less competitive hiring firms as maintaining internal reputation is important everywhere. Recommendations when made within the firm carry most weight when they come from people the hiring manager knows and trusts, so there is a second relationship that you are reliant on - the person you choose to have recommend you needs to carry weight in the right teams.
Try to find someone who works in the right group for your interests first and build up a relationship so you can be sure both you and they are well-matched in the recommendation, even if it means "shopping around" a little. Worst thing is to persuade one person to recommend you on a long shot only to meet someone shortly afterwards who would have been better placed to help you.
All that said, there are ways to find people open to making recommendations - one system mentioned previously on this site is called Mole recommendations (you should find it with a search).