Urban administration in hyper-dynamic cities are being overwhelmed by the scale of public complaints far exceeding current manual management capabilities. Existing citizen complaint websites, offer simple complaint lodges which aren't smart enough to categorize free text complaints, identify critical issues and escalate or dispatch the issue appropriately. This leads to increased resolution times, lack of accountability and poor engagement from citizens. This paper describes the Smart Civic Complaint Analyser, a complete integrated web application that automates the entire citizen complaint lifecycle (submission to resolution) using Machine learning, Natural language processing and Artificial Intelligence. Citizens can lodge complaints with free-text description, images, voice or voice-to-text and GPS tagged location. NLP micro-service with a DistilBART-MNLI based zero-shot classifier, intelligently labels the type of the complaint and assign a priority based on the description, requiring no training with specific labelled task data. A dual-view Citizen-friendly portal with a robust Admin dashboard is served by a React.js front-end, whereas a Node.js/Express.js back-end provides Authentication via JWT and RESTful complaint APIs. User information, complaint history and trails are stored using MySQL and are relayed to users with automated notifications ensuring transparency and timely responses. Functional, integration, performance and usability testing results indicate efficient complaint categorization, faster dispatch of high-priority complaints, integration among modules and improvement in citizen satisfaction. The proposed system reduces administrative efforts, increases speed of resolution and fortifies the citizen-authority communication in smart city administrations.