How to send a response back to client using websockets in AWS Lambda

I am using the Serverless Framework to deploy a WebSocket app to AWS Lambda.

I need to make it send a response back to the client when it hits a WebSocket route.

Here is my handler:

const AWS = require("aws-sdk");

module.exports.websocketHandler = async (event, _) => {
  const {
    requestContext: { routeKey }
  } = event;

  switch (routeKey) {
    case "$connect":
      // ....
      break;

    case "$disconnect":
      // ....
      break;

    case "getBot":
      const body = JSON.parse(event.body);
      const postData = body.data;
      const params = {
        ConnectionId: event.requestContext.connectionId,
        Data: JSON.stringify(postData)
      };

      postMessage(params, event);
      break;

    case "$default":
    default:
      return { statusCode: 200 };
  }

  return { statusCode: 200 };
};

const postMessage = async (data, event) => {
  try {
    const apigwManagementApi = new AWS.ApiGatewayManagementApi({
      apiVersion: "2018-11-29",
      `https://${event.requestContext.domainName}/${event.requestContext.stage}`
    });

    await apigwManagementApi.postToConnection(data).promise();
  } catch (err) {
    console.log(err);
  }
};

It just responds back with whatever was sent. I am using wscat tool to connect to the WebSocket.

wscat -c wss://{API-ID}.execute-api.{REGION}.amazonaws.com/dev
{"action": "getBot", "data": "Hello world"}

I have tried testing it offline, and it works just fine. And when deployed, I can connect to it, but whenever I try to send the action to getBot, I get no response.