diff --git a/test/node-test/client-dispatch.js b/test/node-test/client-dispatch.js
index d780da3b7b9..55713d9ad0e 100644
--- a/test/node-test/client-dispatch.js
+++ b/test/node-test/client-dispatch.js
@@ -3,6 +3,7 @@
 const { test } = require('node:test')
 const assert = require('node:assert/strict')
 const http = require('node:http')
+const https = require('node:https')
 const { Client, Pool, errors } = require('../..')
 const stream = require('node:stream')
 const { createSecureServer } = require('node:http2')
@@ -959,3 +960,91 @@ test('dispatches in expected order for http2', async (t) => {
 
   await p.completed
 })
+
+test('Issue#3065 - fix bad destroy handling', async (t) => {
+  const p = tspl(t, { plan: 4 })
+  const server = https.createServer(pem, (req, res) => {
+    res.writeHead(200, { 'content-type': 'text/plain' })
+    res.end('ended')
+  })
+
+  server.listen(0, () => {
+    const client = new Client(`https://localhost:${server.address().port}`, {
+      connect: {
+        rejectUnauthorized: false
+      }
+    })
+
+    t.after(closeClientAndServerAsPromise(client, server))
+
+    const dispatches = []
+    const dispatches2 = []
+
+    client.once('disconnect', (...args) => {
+      const [,, err] = args
+      p.strictEqual(err.code, 'UND_ERR_INFO')
+      p.strictEqual(err.message, 'servername changed')
+    })
+
+    client.dispatch({
+      path: '/',
+      method: 'POST',
+      body: 'body'
+    }, {
+      onConnect () {
+        dispatches.push('onConnect')
+      },
+      onBodySent () {
+        dispatches.push('onBodySent')
+      },
+      onResponseStarted () {
+        dispatches.push('onResponseStarted')
+      },
+      onHeaders () {
+        dispatches.push('onHeaders')
+      },
+      onData () {
+        dispatches.push('onData')
+      },
+      onComplete () {
+        dispatches.push('onComplete')
+        p.deepStrictEqual(dispatches, ['onConnect', 'onBodySent', 'onResponseStarted', 'onHeaders', 'onData', 'onComplete'])
+      },
+      onError (err) {
+        p.ifError(err)
+      }
+    })
+
+    client.dispatch({
+      servername: 'google.com',
+      path: '/',
+      method: 'POST',
+      body: 'body'
+    }, {
+      onConnect () {
+        dispatches2.push('onConnect')
+      },
+      onBodySent () {
+        dispatches2.push('onBodySent')
+      },
+      onResponseStarted () {
+        dispatches2.push('onResponseStarted')
+      },
+      onHeaders () {
+        dispatches2.push('onHeaders')
+      },
+      onData () {
+        dispatches2.push('onData')
+      },
+      onComplete () {
+        dispatches2.push('onComplete')
+        p.deepStrictEqual(dispatches2, ['onConnect', 'onBodySent', 'onResponseStarted', 'onHeaders', 'onData', 'onComplete'])
+      },
+      onError (err) {
+        p.ifError(err)
+      }
+    })
+  })
+
+  await p.completed
+})