Valmiki Ramayana Yuddha Kanda Sarga 111 Shloka 21

हतस्य killed, जीवितात् life, भ्रश्यमानस्य fallen from, तस्य his, हस्तात् hand, ससायकम् arrow, कार्मुकम् bow, आशु with, प्राणैःसह with life breath, निपपात fell

Thus, when Ravana was killed and lost his life, the bow and arrow in his hand also fell along with his life breath.