A novel refractive index sensing using the tapered single mode fiber (TSMF) is proposed based on the chaotic correlation fiber loop ring down system (FLRDs). A chaotic fiber laser is used to drive the fiber loop cavity. The performance of the proposed TSMF chaotic correlation FLRDs refractive index sensing was demonstrated by measuring the ring down time of the peaks of correlation coefficient of the sensing system at different refractive index. The sensing demonstrates a good stability and repeatability. The influence of the change in fiber loop length on the sensing system was also investigated. The results show that the sensitivity of chaotic correlation FLRDs increases with the decrease of the loop length and the change of the loop length has little effect on the detection limit (DL) of the system. The DL of 10-4 RIU were achieved. Compared with the pulsed FLRDs, the chaotic correlation FLRDs significantly simplify the light source of sensing system and eliminate the trade-off problem between the length of fiber loop cavity and the light source, and makes fiber loop length more flexible.