Gift splitting comes into play (typically) when the gifted property is held individually (i.e., as separate property); the spouse who owns the property (separately) can elect to split the gift so one-half is treated as given by her and one-half is treated as given by her spouse.
With respect to gifts made where the property is held as community property (or certain property considered to be jointly held), the gift is considered to be made one-half by each spouse.
