Shopping around for a car? You're in luck. Shopping around for a new auto insurance policy? Better buckle up.New, used and even rental car prices continue to slide while car insurance rates remain vastly elevated. That diverging trend seems counterintuitive: If the price tag for a car has gone down, shouldn't the cost to insure it go down too?If only it were that simple."It's a mosaic of factors that impact auto insurance costs," said Scott Shapiro, who leads KPMG's U.S. insurance division. "While there is a general correlation between the price of the vehicle and insurance as it relates to physical damage, there are other factors beyond the price of the car that impact premium costs."For instance, almost 41,000 people died in car crashes last year — 8,000 more fatalities compared to 2013, the National Highway Traffic Safety Administration estimated. That's led to an increase in claims that are well above historical dollar amount averages because of their severity, according to LexisNexis Risk Solutions data.Relief could be on the wayCar insurance rates are up 18.6% for the 12 months ended in July, according to Consumer Price Index data released Wednesday. That marked the third-largest jump in prices over the past year across all goods and categories that CPI tracks.Still, that's an improvement from March, when car insurance rates were up 22.2% annually. The last time car insurance rates rose that much on an annual basis was in 1976.But just like the overarching inflation across the economy, where the pace of price increases has cooled, the actual dollar amount consumers are paying for goods and services is much higher than in recent years. However, with cars, consumers are paying lower prices. That means price increases didn't just slow down, car prices actually dropped.Used car prices fell by 10.9% over the past year, marking the third-largest drop in prices across all goods and categories that the CPI tracks. Rental and new cars also got cheaper, with prices falling by 6.2% and 4.4%, respectively.The steep fall in used car prices is a "direct reflection" of the new car market, Ivan Drury, the director of insights at Edmunds, said in an analysis published Wednesday. Dealerships are taking longer to sell new cars compared to a year ago, resulting in discounts that are $1,000 higher on average. "A buildup of new vehicles on lots over the past year has been the catalyst for discounts and incentives on aging inventory," he added.Eventually, this could translate into lower insurance rates, said Josh Damico, vice president of insurance operations at Jerry, a car insurance savings app."Car insurance premiums lag contributing factors such as prices for vehicles and repairs, so insurers have been playing catch-up over the past year or so," Damico told CNN. Auto repair costs, while up 3.4% compared to a year ago, have cooled significantly from last July when they were rising at a 12.7% rate annually, according to CPI data.With both those costs leveling off, "many insurers are reevaluating their pricing, with some already lowering their rates," he said.