Is it true that Mazda parts are more expensive than those of comparable cars?

One publication to check dependability is "Consumers Reports Buyers Guide", which can be found in public libraries.

There is no reason to worry about cost of parts that don't break very often. The items to be concerned about are normal wear items (brake pads, shoes and tires to name a few). If it doesn't take some weird tire size then tire cost is negligible. I have a buddy with a Toyota (true it is a sports version) that he can not find tires for. But with a Mazda that is not a problem.

The place Mazda got a bad rep was with the R model vehicles. "R" designated a rotary engine and "M" meant it had a regular engine. The rotary engines suffered from uniformed owners who never learned how to operate one. The piston engine powered cars made by Mazda were and are very dependable. The CX-3 has a pistion engine, so there should be no unusual problems. 

No.

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The cost of the replacement parts is only one part of the equation.  The other consideration is how often you actually need to replace those parts...

If the vehicle is generally reliable, it is still cheaper to own compared to another brand of vehicle which may have cheaper parts but needs those parts replaced more often.

This is opinion, without part to part price comparisons. My Toyota Camry parts ALL cost more than my Mazda's parts. My Jeeps parts cost less yet, and I needed fewer of them.

Less common makes generally have less aftermarket parts, so it would be more expensive. I had this problem with my old Mitsubishi Eclipse. Makes like Honda, Toyota, Nissan, Kia, Hyundai, Chevy, dodge, ford, tend to have cheaper parts. 

I don't know that data you seek exists.

There is data from 10 years of maintenance

https://autowise.com/carmakers-with-the-highest-ma...

Mazda is moderately low cost.

Mazda CX-3 rated OK here

https://repairpal.com/reliability/mazda/cx-3

As a used subcompact SUV priced $15K-$20K, the 2017 Mazda CX-3 ranked tied #3/4/5, which is pretty good.

https://cars.usnews.com/cars-trucks/rankings/used/...

Edmunds.com has estimates of value based on detail.

It is noted for its safety and performance and cost of ownership and critics ratings , but in this shows only 3/5 for JD Power reliability.

Safe cars may tend to absorb impacts and require more extensive repairs in crashing, but the goal is being people safe.

It gets #1 in 2017 Affordable Subcompact SUVs

There is discussion in blogs that Mazda factory parts are more expensive than other Japanese brands. From what I can tell, Mazda CX-3 is an imported vehicle from Japan, rather than USA produced. Japanese brand models are sometimes USA made and parts could therefore cost less.

The data is spotty, and note that most repair cost is labor rather than parts.

Do you do all your own service?

Do you service at the dealership or at an aftermarket shop?

I remember I had a Mazda 626 a long time ago, and it was a decent car.

I can't judge cost of parts since I don't know competing. 

i would go to a place that sells them and ask them about it