She may have been thinking you would be reluctant to call the police because of the swinging aspect.
Yes but you seem to be missing the crux of the story here: she also stole our car. 
Was she a Russian Poker player by any chance?
Or a Jewish heiress to a junk mail fortune. Who forgets to call in a timely manner. Theft would be her next failing.
You are burying the lede here. Let’s hear more about the swinging!
Probably not, because the justice system in this country is so messed up.
My car was stolen & totaled (rolled several times, with drugs & sawed-off shotgun inside) and nothing serious happened to the thief.
Wow. Swinging and stolen vehicles and this lost my interest after about 10 posts. You need to try harder!
The “swinging” thing would be none of the cops’ business. All they needed to tell the officers is that she was (WAS!) a friend, and that’s it.
That would have been a bad idea. Because now when the police catch her with the car, she will tell them that you gave her permission to keep the car for a few days but you’re denying it now because of some jealousy over the swinging part. And when the police come back to you and ask about the swinging part and you admit that was true but you wanted to conceal it, how much credibility do you think you will have when you insist the part about her stealing the car was true?
Why are you still here, posting even? Kinda makes it hard to believe your sooooo disinterested. You try harder! 
Yes, because I have exhibited even the slightest similarity to Shagnasty on quite a few occasions, I know. This is a very spot-on and frankly pretty damn witty remark.
Shagnasty would have told us what her rating was on a scale of 1-10.
Someone stole my old Dodge pickup. Parked it outside my father’s business, came outside to run an errand and it was gone. Reported it stolen to the sheriff. 3 days later it is spotted by a Tacoma cop and he tries to pull the guy over, he runs into a fire hydrant instead. The thief claimed I left the keys in the ignition so he could drive it. You did not need a key to start the truck, I used a screwdriver to turn the broken ignition switch. He broke a wing window to get in and hot wired it to steal it.
He got 9 months in jail, I had to fix the wing window and replace the front bumper and the bent front axle. Plus I installed a new ignition switch.
I agree with nearwildheaven; they knew her & let her borrow the car for an errand, not to take it for days. They fact that they knew her in the Biblical sense rather than the more common parlance of ‘knew’ is immaterial.
tvaetbjorn, why was the car towed & cost you $? Because she left it on private property & was towed to a private lot or did the government tow it, either because it was parked illegally or to secure it? Seems sucky to make a crime victim pay to get their property back if it was the latter. Isn’t that the definition of extortion?
“Oh, uh… I guess there weren’t any keys… yeah, now I remember, he left the screwdriver in the ignition!”
Like I said, it’s a credibility issue. Unless the woman chooses to confess her guilt when the police catch her, it’s going to be a case of what you say versus what she says. Finding out you were lying about some of your story isn’t going to help you convince people you were telling the truth about the rest of your story.
Statement to police: “We invited {car thief} over, she wanted to get cigarettes, I told her she could use my car instead of walking. She never returned despite numerous text messages asking her to bring it back. I/We’d like to press charges for vehicle theft.”
Whether they invited her over to look at vacation pics, play board games, or have wild, kinky sex is an immaterial detail. Showing the PD their phone, w/ a text message saying, “please bring my/our car back” only furthers to back up their story & the timeline of that story.
Yep, she’s for sure gonna say, " they loaned it to me. I never got the texts".
“Wow, that was the worst sex of my life. The guy didn’t even get up to see me out. I’m gonna steal his damn car.”
Unless you’re the mayor, you don’t have the option of summoning the police, telling them only what you choose to tell them, and dismissing them with an offhand “Now go fetch my car like good minions.”
What happens with the rest of us is you call the police and report the crime. They will show up and they will ask you questions about the crime including the suspect if you can identify one. And “How do you know this person?” is going to be one of those questions.
Now you can be evasive if you want to try it. But the police are going to notice you’re evading the question. Or you can try straight-up lying.
Either way, when the police catch up with this woman and your car, she’s probably going to tell them a story rather than admit she stole your car. She’ll say “Yeah, they invited me over to their house for a threeway. The guy is my old boyfriend and we get along great. So I asked if I could borrow his car for a few days and he said yes. But his wife is jealous because she knows he likes me better than her. So they started arguing about him loaning me the car. Well, I didn’t want to stick around for that and he had already given me his permission and the keys so I left. Anyway after I left she must have convinced him to say I stole the car to get me in trouble.”
Now at this point, it’s a case of what you’re saying versus what she’s saying. And that part earlier, where you were being evasive? That’s going to count against the police believing you. And if you tried lying and told the police she just came over for a round of board games, it’s going to go worse. And if you try to keep lying and still deny there was any sex, she’ll ask for a medical exam. After that, you might be facing criminal charges yourself.