Crispy, honey, your fears are misplaced. The police WILL believe you just as we've believed you from the outset - where, if you look back, you'll find you didn't say very much at all but you didn't need to because we know that no woman in her right mind would make a false claim of rape and, although it may not seem that way to you at times, if there's one thing you are it's in your right mind.
As for having 'fucked up by not reacting properly', there is no 'proper' way to react to having been raped. As the police and other authorities are well aware, every victim of this heinous crime reacts differently.
I also want to disabuse you of any notion that you are 'naive and stupid and gullible'. How long is it since you joined mumsnet? No-one who reads the Relationships and AIBU boards can stay in a state of ignorance or unsullied bliss for very long. The mentally sick, the twisted, the perverted... all huMAN life is here and a day on this board is worth a year poring over psychiatry/psychology tomes - and a helluva lot more amusing educational. 
If you were naive or gullible or stupid or all 3 on that night, Crispy, it was because you dropped your guard for one reason, and one reason only: he abused the trust that ANY WOMAN, or any man for that matter, would unquestionably place in a PARAMEDIC.
He takes advantage of his position as one of society's widely regarded heroes to take advantage of those women that he deliberately targets because he knows he possesses the physical power to easily overcome their resistance to his sexual advances.
He's certainly cunning but, given that many perpetrators convict themselves within a short time of being taken to a police station for questioning, it remains to be seen if he's clever - and it may transpire that he's too clever for his own good.
But having cautioned you not to do so, I'm in danger of getting ahead of myself as it may be that the result of you making a statement could fall far short of what you hope/fear may happen.
It that should occur, please rest assured that it WON'T be because one or more police officers don't believe you. It WILL be because the CPS, in their infinite wisdom 
decide there is insufficient evidence to prosecute.
As AF has said, there is the not inconsiderable matter of 'burden of proof' and it won't be in your best interests for the powers that be to proceed to a trial where the presumption is that a 'not guilty' verdict is something of a foregone conclusion.
Again, this wouldn't mean you have not been believed - far from it, honey, and if this should occur it's likely that those who've heard your testimony will be determined to nail him a future date tearing their hair out.
What I'm trying to say in my usual long-winded manner is that, no matter what the outcome, making a statement to the police will put you in a win-win position and, even if he is not brought in for questioning, you can rest assured that his card will be well and truly marked for reasons that I will expound on in a later response.
This will be the first time you have talked about your ordeal in rl to those who are specially trained to hear you and act on what you are saying. You will find it at times a relief to be able to unburden yourself and at times distressing as you re-live what he did to you, but you will also find it empowering to have dug deep and found the courage to do what naice well-mannered girls are brought up to do - which is tell the truth and shame the devil 
Before you go to give your statement later today. I strongly urge you to write out a short account of the events of that night incorporating the, now 8, points I've outlined together with any others that come to your mind, and take it with you as a reminder of the salient facts which are key to any subsequent police investigation
It can be the case that victims feel inhibited or intimidated by the very fact that giving a statement to the police is not an experience they are accustomed to. When giving your account, take your time. When asked questions, don't rush to answer; think about what you've and if you can't recall/don't know, don't be afraid to say so. You have NOTHING to fear, honey, as I know your honesty will shine through.
My apologies again to aleene - in my anxiety not to put, or have words put, into your mouth, Crispy, I didn't appreciate how rude and overbearing my response to her post must have appeared to others.
Given my advice for you to write down certain key points, that may come across as gross hypocrisy on my part but my concern is that you should give your account in your own words while not omitting anything which can assist the police in establishing this man's modus operandi.
You're not going to be alone, Crispy, we are all going to be with you - reach out and draw on our strength and you'll feel our hands holding yours.