Deciphering how neural circuits are anatomically organized with regard to input and output is instrumental in understanding how the brain processes information. For example, locus coeruleus noradrenaline (also known as norepinephrine) (LC-NE) neurons receive input from and send output to broad regions of the brain and spinal cord, and regulate diverse functions including arousal, attention, mood and sensory gating. However, it is unclear how LC-NE neurons divide up their brain-wide projection patterns and whether different LC-NE neurons receive differential input. Here we developed a set of viral-genetic tools to quantitatively analyse the input-output relationship of neural circuits, and applied these tools to dissect the LC-NE circuit in mice. Rabies-virus-based input mapping indicated that LC-NE neurons receive convergent synaptic input from many regions previously identified as sending axons to the locus coeruleus, as well as from newly identified presynaptic partners, including cerebellar Purkinje cells. The 'tracing the relationship between input and output' method (or TRIO method) enables trans-synaptic input tracing from specific subsets of neurons based on their projection and cell type. We found that LC-NE neurons projecting to diverse output regions receive mostly similar input. Projection-based viral labelling revealed that LC-NE neurons projecting to one output region also project to all brain regions we examined. Thus, the LC-NE circuit overall integrates information from, and broadcasts to, many brain regions, consistent with its primary role in regulating brain states. At the same time, we uncovered several levels of specificity in certain LC-NE sub-circuits. These tools for mapping output architecture and input-output relationship are applicable to other neuronal circuits and organisms. More broadly, our viral-genetic approaches provide an efficient intersectional means to target neuronal populations based on cell type and projection pattern.