Yes...it is possible. There are a couple of ways of addressing the "one-to-many" scenario with dapper:

METHOD 1 - Return two queries, combine in DAL

ALTER PROCEDURE [dbo].[GetCarData]
    @CustomerID int, 
    @Year int
AS
BEGIN
    SET NOCOUNT ON;

    --return cars
    SELECT c.*
        from [dbo].Car c
    INNER JOIN [dbo].Customer cust ON c.CarID = cust.CarID
    WHERE cust.CustID = @CustomerID AND cust.Year = @Year

    --return options
    SELECT opt.*
        from [dbo].Car c
    INNER JOIN [dbo].Customer cust ON c.CarID = cust.CarID
    INNER JOIN dbo.CarOptions opt ON op.CarID = c.CarID
    WHERE cust.CustID = @CustomerID AND cust.Year = @Year

END

DAL

var multi = db.QueryMultiple(getCarDataSp , new { CustomerID = customerId, Year = year },
                                commandType: CommandType.StoredProcedure));

var cars = multi.Read<CarDTO>();
var options = multi.Read<CarOptionDTO>();

//wire the options to the cars
foreach(var car in cars){
    var carOptions = options.Where(w=>w.Car.CarID == car.CarID);        //I would override Equals in general so you can write w.Car.Equals(car)...do this on a common DataModel class
    car.Options = carOptions.ToList();
}

METHOD 2 - Return one query, split in DAL

Proc

ALTER PROCEDURE [dbo].[GetCarData]
    @CustomerID int, 
    @Year int
AS
BEGIN
    SET NOCOUNT ON;


    SELECT c.*,  opt.*
     from [dbo].Car c
    INNER JOIN [dbo].Customer cust ON c.CarID = cust.CarID
    LEFT OUTER JOIN dbo.CarOptions opt ON op.CarID = c.CarID
    WHERE cust.CustID = @CustomerID AND cust.Year = @Year

END

DAL

var tuples = db.Query<CarDTO, CarOptionDTO,Tuple<CarDTO,CarOptionDTO>>(getCarDataSp , new { CustomerID = customerId, Year = year },
(car,opt)=> Tuple.Create(car,opt),                       commandType: CommandType.StoredProcedure);

//group tuples by car
var cars = tuple.GroupBy(gb=>gb.Item1.CarID)                    //again, overriding equals makes it so you can just to GroupBy(gb=>gb.Item1)
            .Select(s=>{
            var car = s.First().Item1;
            var carOptions = s.Select(t=>t.Item2).ToList()

            return car;
            });

Enhancements

Using a temp table in the query

This puts all filtering by parameters into a single query. Subsequent queries are drop-dead simple selects by ID.

ALTER PROCEDURE [dbo].[GetCarData]
    @CustomerID int, 
    @Year int
AS
BEGIN
    SET NOCOUNT ON;

    declare @t table(CarID int);

    --filter cars (only deal with parameters here)
    INSERT INTO @t(CarID)
    SELECT c.CarID
    FROM dbo.Car c
        INNER JOIN [dbo].Customer cust ON c.CarID = cust.CarID
    WHERE cust.CustID = @CustomerID AND cust.Year = @Year

    --return cars
    SELECT c.*
    FROM [dbo].Car c
        INNER JOIN @t t ON t.CarID = c.CarID

    --return options
    SELECT opt.*
    FROM dbo.CarOptions opt
        INNER JOIN @t t ON t.CarID = opt.CarID

END

Applying a BaseDTO to help with equality

Once you have the BaseDTO, and wire up your ID you can simply say things such as:cars.Where(w=>w.Equals(car)), dictionary[car] (if it's in there), if(car.Equals(otherCar)), or results.GroupBy(gb=>gb.Car)...

public class BaseDTO
{
    internal int ID { get; set; }

    /// <summary>
    /// If the obj is the same type with the same id we'll consider it equal.
    /// </summary>
    public override bool Equals(object obj)
    {
        if(obj == null || this.GetType() != obj.GetType())
        {
            return false;
        }

        return this.GetType().GetHashCode() == obj.GetType().GetHashCode() &&
                this.ID == (BaseDTO)obj.ID;
    }

    /// <summary>
    /// If you override equals, you should override gethashcode.  
    /// http://stackoverflow.com/questions/263400/what-is-the-best-algorithm-for-an-overridden-system-object-gethashcode#263416
    /// </summary>
    public override int GetHashCode()
    {
        unchecked
        {
            int hash = 17;

            hash = hash * 23 + this.GetType().GetHashCode();
            hash = hash * 23 + this.ID;

            return hash;
        }
    }
}

public class CarDTO : BaseDTO
{
    public int CarID
    {
        get { return this.ID; }
        set { this.ID = value; }
    }
    public string Manufacturer { get; set; }
    public List<CarOptionDTO> CarOptions { get; set; }
}