You must allocate the rental portion and the personal portion of your vehicle expense since you used the car for both purposes. For example, if you drove straight to your rental property, only mileage to the property and back is your rental purpose or only mileage for rental purposes is deductible. Compare this against your total mileage driven, and you will have the ratio of rental vs. personal use.
As to the gasoline part - you can deduct standard miles or actual expenses when claiming vehicle expenses. If you choose to deduct actual miles, then you can deduct the gasoline (and, of course, the rental portion as I explained above). If you choose to use standard mileage method (.54 cents per mile), the gasoline is included in the standard mileage rate, you cannot deduct it separately.
