Compute-in-memory (CIM) is a promising approach for realizing energy-efficient deep neural network (DNN) accelerators. Previous CIM works focusing on uniform quantization (UQ) demonstrated a higher Multiply-accumulate (MAC) precision requirement to maintain DNN inferencing accuracy, resulting lower energy efficiency. The nonuniform quantization (NUQ) has proved to require lower precision than UQ, while the existing implementations are based on high precision digital lookup table (LUT) (e.g., 16-bit), leading to large energy and area overhead for multiplier. This work presents CLUT-CIM fabricated under 28-nm CMOS featuring: 1) a capacitance LUT (CLUT)-based NUQ MAC circuit with thermometer coding scheme for weight and input activation that avoids digital LUT and reduces the energy and area overhead; 2) a signed-channel training (SCT) method that reduces the switching activity of computation to improve the energy efficiency; 3) a dual-port 6T-SRAM array to enable simultaneously weight updating and CIM operations, enhancing the memory utilization and CIM throughput. Under 3-bit NUQ precision, the peak energy efficiency is 114.3 TOPS/W, and peak throughput density is 31.78 TOPS/mm $^{2}$ .