If you rent from a Jewish company you must ask the renter if they did a Bedikah in the cars. If there is no one to ask it is enough if you do Bitul only. However, if you rent from a Non-Jew then you will need to do a Bedikah.
Explanation:
The Gemara in Pesachim 4a:
They asked Rav Nachman bar Yitzchak one who rents his house to a friend on the fourteenth who is obligated to the Bedikah? Is the owner since it is his Chametz, or the renter since the chametz will be in his property? Rav Nachman bar Yitzchak answered we learned one who rents a house to his friend and didn’t give him the keys yet then he has to do the Bedikah, but if he gave him the keys before the fourteenth then the renter has to.
The Gemara continues: They asked Rav Nachman bar Yitzchak what if one rents a house on the fourteenth can he assume the house is checked or no? Why not just ask him? He is not around, so does he need to do a Bedikah? …he can assume that it was checked.
The Rishonim argue whether the renter has to check the house if he has the keys before the fourteenth but dint enter the house. Since he didn’t start his renting, so he doesn’t have to, or only if he entered.
The Ran sys if he rented the house for the fourteenth and on, if he didn’t get the key unit the fourteenth … It is no to say that e giving the key creates a transaction which starts his renting since we know that land (renting land as well) cannot possessed unless he gives money, a Shtar, or through a chazakah (show o ownership like locking the door), not giving the keys. The point is the even if he made a Kinyan since the chametz it is the owner’s and the owner has the key the owner has to check. Unless he takes the key and enters before the fourteenth. (The Maggid Mishnah agrees as well) the renter that also make a Kinyan to be obligated in a Bedikah.
The Tosfot sys the we are discussing where he has the key but dint do a Kinyan it just depends how has the key at sundown of the fourteenth he has to enter and do a Bedikah.
The Chatam Sofer explains that according to Tosfot the main reason for Bedikah is because maybe he will eat it so it is relay on the renter, but if the chiyuv starts on the owner then he cannot exempt himself by passing the key. However, since the basic obligation is on the renter then even without a kinyan just give the key he must check.
According to the Ran the main obligation is on the owner maybe he didn’t do a Bitul on his chametz and he will transgress Bal Yeraeh, and the renter just ahs to do a bedikah since he is n the house. As long as the renter didn’t take control of the house it is not his obligation even if he has the key.
The Shulchan Aruch 416:1: One who rents his house from the fourteenth and through Pesach and he did a Kinyan, if he does not have the key by sundown of the fourteenth then the owner has to check but if he had the key by sundown he has to check.
Like the Ran that the key is what creates the obligation.
In our case you are renting the car on Chol HaMoed itself it is obvious that the obligation falls on the head of the owner. However, do we need to ask the owner or can we rely on a Chazaka that he did a bedika? Also, can we rely on the cleaning they do after each use?
The Shulchan Aruch 437:2 : one who rents the house on the fourteenth he doesn’t know if there was a bedikah done to the house. If the owner is in the city then we must ask him otherwise we can assume he did the Bedikah and a bitul.
The Shulchan Aruch rules that if he does not know then he can try to ask the owner if he can’t then we say it was checked. The fore if he rents from a Non jew then is almost certain that it wasn’t checked and he would have to do Bedikah.
Even though the Rambam hold that generally when someone rents something and an object is left there it belongs to the owner. If that is true then the he would not o have to do Bedikah at all. The Shulchan Aruch rule that the renter can also get lost objects.
Whether one may relay on the cleaning the car has after each person. We can’t. The Ran 433 writes that the minhag is clean up for a the Bedikah. A Bedikah is required even or a clean house.
The same thing applies s by hotels. if he rents the room because the fourteenth then he must do Bedikah, even if they cleaned it before each person. So ruled R’ SZ Auerbach.
If he rents from a Jew then he must ask him, if he can’t then he just do Bitul and it is fine.