Spiking Neural Networks (SNNs) are efficient computation models to perform spatio-temporal pattern recognition on {resource}- and {power}-constrained platforms. SNNs executed on neuromorphic hardware can further reduce energy consumption of these platforms. With increasing model size and complexity, mapping SNN-based applications to tile-based neuromorphic hardware is becoming increasingly challenging. This is attributed to the limitations of neuro-synaptic cores, viz. a crossbar, to accommodate only a fixed number of pre-synaptic connections per post-synaptic neuron. For complex SNN-based models that have many neurons and pre-synaptic connections per neuron, (1) connections may need to be pruned after training to fit onto the crossbar resources, leading to a loss in model quality, e.g., accuracy, and (2) the neurons and synapses need to be partitioned and placed on the neuro-sypatic cores of the hardware, which could lead to increased latency and energy consumption. In this work, we propose (1) a novel unrolling technique that decomposes a neuron function with many pre-synaptic connections into a sequence of homogeneous neural units to significantly improve the crossbar utilization and retain all pre-synaptic connections, and (2) SpiNeMap, a novel methodology to map SNNs on neuromorphic hardware with an aim to minimize energy consumption and spike latency.