1996 355 challenge car, can it have a title?

I believe 348 and 355 challenge cars were converted street cars.

 

348s come with titles. 355s as a general rule do not.

 

I own a 348 challenge car and it has a title. I can't say about the 355 challenge, cause I don't have one.

 

You are correct.

 

That's correct. There are some states in which it's easier than others to get a car titled, but only 348 & '95 355 Challenge cars initially had titles- anything thereafter was imported on an MSO only, so it'd be tough to get a title anywhere. The VIN (they do have a 17-digit VIN) would be kicked back by the titling authorities as noncompliant.
Even if you do buy a Challenge car with a proper title few states will give you tags for a car lacking things like an exhaust, turn signals, horn, etc., and having things like a roll cage. Even if you were to retro-fit the MANY required items (and remove the forbidden ones) you may still have problems. My car still has the original sticker on the cage that says, in effect, you may never drive a Challenge car on the street, at least not without having the dealer return the car to its original specifications.

 

To repeat/add to Ira's comments above, it wouldn't be impossible to get a title for one of the '97 or '98 factory cars in some states. There are quite a few that have kit car rules and I would imagine a person could use that concept. I had my serial no.('97 355 factory CH)run thru a DMV data base, in CA and MT, and no flags came up. I am assuming the EPA didn't care much about the few cars that came into the US after they were here and originally went though their cross hairs.
On my MSO for my car it states that the car is a "1997 F355 B CHALLG" but it also states "This vehicle conforms to US EPA and State of CA regulations applicable to 1994 Model Year New Motor Vehicle." That contradiction of years is going to throw even the dimmest bulb behind the counter at your local DMV but with all that said there are ways to get one titled.
Maybe the answer to the OPs question could be; if the car is a '96 it could have been a road car converted(which would mean it had a title) for the challenge series Ferrari had rules that allowed for later road(after '95) cars to be converted.

 

The '97 and '98 were even more complete with race kit from the factory instead of it coming in a box as the later 348s. IIRC they came with the brembo brakes, roll cage, seat, suspension parts installed, wheels, air bags removed, frt euro bumper, (the rear light weight bumper was optional) tow hooks and modified exhaust. The CH cars even had a specific wiring harness. Of course Ferrari upped the anti on the number of non street parts that were on the 355s than on the 348 so maybe they thought it was easier to complete the cars at the factory instead of rebuilding them at the dealer or at FNA. There was a "kit" in '98 that was installed by the dealer which included the rear wing, trans oil cooler,modified roll cage and other smaller items and a rule change that allowed the cars to be lightened(heater ac head light removal etc.)