Dr Monzer Kahf, a prominent Muslim economist and counsellor, states that: “In leasing, the owner/lessor is always responsible to make the leasehold (the car in the case in hand) available to the user/lessee in working conditions. This means that insurance, taxes and basic maintenance must be in principle the responsibility of the owner/lessor.
However, in leasing the two parties can determine the rental amount in any way they like; i.e. the rental may be in money e.g., a given monthly payment for certain number of months or a down payment at the date of the contract plus a monthly amount, and it can be a service such as you provide me with the insurance service according to certain known specifications, or a combination of both. The reason is that in Shari’ah the rental amount must be known at the time of contract, and as long as it is known, it can be in kind (a commodity or a service) or in money.
Insurance can normally cover essential maintenance, not related to operation, such as all the maintenance responsibility of the owner/lessor. Further a great part of the insurance in cars relates to the user/operator and her/his style of driving etc.
The important result of this discussion is that in a leasing agreement, insurance service, a down payment, and a monthly payment for a given number of months can be combined together as being the rental amount. Hence, in my opinion insurance and taxes can be on the lessee provided this is mentioned in the contract.