There are Lakota made turtle dance sticks similar to this example, but while this is definitely Native American, perhaps Lakota, it has no provenance.  It is likely from the 2nd half of the 20th C, no earlier, and like many of their products these were made for both actual use in ceremonies/dances, but also offered for sale.  It measures approx 171/2" L, the skull measuring approx 3" L x 2 1/2" W x 1 1/2" D, no damage, no repairs, as originally used.  The wrapped cloth on the handle us a but loose near the hand held end, but complete.  There are no odors.  I include this quote from an online gallery speaking of the use of turtle skulls and shells in their traditional work.  (The snapping turtle is not endangered.)

"The spirit of the turtle (keya) teaches us patience to help others; determination to accomplish your goals; and ability to be strong during difficult times. Turtle goes inside his shell, to show us to reflect and improve the inner you."

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