diff --git a/src/cloud-sql-instance.ts b/src/cloud-sql-instance.ts
index 496cab5..f316e30 100644
--- a/src/cloud-sql-instance.ts
+++ b/src/cloud-sql-instance.ts
@@ -69,6 +69,7 @@ export class CloudSQLInstance {
   private scheduledRefreshID?: ReturnType<typeof setTimeout> | null = undefined;
   /* eslint-disable-next-line @typescript-eslint/no-explicit-any */
   private throttle?: any;
+  private closed = false;
   public readonly instanceInfo: InstanceConnectionInfo;
   public ephemeralCert?: SslCert;
   public host?: string;
@@ -106,17 +107,45 @@ export class CloudSQLInstance {
     }) as ReturnType<typeof pThrottle>;
   }
 
-  forceRefresh(): Promise<RefreshResult> {
+  forceRefresh(): Promise<void> {
     // if a refresh is already ongoing, just await for its promise to fulfill
     // so that a new instance info is available before reconnecting
     if (this.next) {
-      return this.next;
+      return new Promise(resolve => {
+        if (this.next) {
+          this.next.finally(resolve);
+        } else {
+          resolve();
+        }
+      });
     }
+
     this.cancelRefresh();
-    return this.refresh();
+    this.scheduleRefresh(0);
+
+    return new Promise(resolve => {
+      // setTimeout() to yield execution to allow other refresh background
+      // task to start.
+      setTimeout(() => {
+        if (this.next) {
+          // If there is a refresh promise in progress, resolve this promise
+          // when the refresh is complete.
+          this.next.finally(resolve);
+        } else {
+          // Else resolve immediately.
+          resolve();
+        }
+      }, 0);
+    });
   }
 
   refresh(): Promise<RefreshResult> {
+    if (this.closed) {
+      this.scheduledRefreshID = undefined;
+      this.next = undefined;
+      return Promise.reject('closed');
+    }
+
     const currentRefreshId = this.scheduledRefreshID;
 
     // Since forceRefresh might be invoked during an ongoing refresh
@@ -183,6 +212,12 @@ export class CloudSQLInstance {
   // used to create new connections to a Cloud SQL instance. It throws in
   // case any of the internal steps fails.
   private async performRefresh(): Promise<RefreshResult> {
+    if (this.closed) {
+      // The connector may be closed while the rate limiter delayed
+      // a call to performRefresh() so check this.closed before continuing.
+      return Promise.reject('closed');
+    }
+
     const rsaKeys: RSAKeys = await generateKeys();
     const metadata: InstanceMetadata =
       await this.sqlAdminFetcher.getInstanceMetadata(this.instanceInfo);
@@ -244,6 +279,9 @@ export class CloudSQLInstance {
   }
 
   private scheduleRefresh(delay: number): void {
+    if (this.closed) {
+      return;
+    }
     this.scheduledRefreshID = setTimeout(() => this.refresh(), delay);
   }
 
@@ -260,4 +298,11 @@ export class CloudSQLInstance {
   setEstablishedConnection(): void {
     this.establishedConnection = true;
   }
+
+  // close stops any refresh process in progress and prevents future refresh
+  // connections.
+  close(): void {
+    this.closed = true;
+    this.cancelRefresh();
+  }
 }
diff --git a/src/connector.ts b/src/connector.ts
index c152ebd..acde4a7 100644
--- a/src/connector.ts
+++ b/src/connector.ts
@@ -230,8 +230,8 @@ export class Connector {
             serverCaMode,
             dnsName,
           });
-          tlsSocket.once('error', async () => {
-            await cloudSqlInstance.forceRefresh();
+          tlsSocket.once('error', () => {
+            cloudSqlInstance.forceRefresh();
           });
           tlsSocket.once('secureConnect', async () => {
             cloudSqlInstance.setEstablishedConnection();
@@ -333,7 +333,7 @@ export class Connector {
   // Also clear up any local proxy servers and socket connections.
   close(): void {
     for (const instance of this.instances.values()) {
-      instance.cancelRefresh();
+      instance.close();
     }
     for (const server of this.localProxies) {
       server.close();
diff --git a/test/cloud-sql-instance.ts b/test/cloud-sql-instance.ts
index 5ce311d..1932902 100644
--- a/test/cloud-sql-instance.ts
+++ b/test/cloud-sql-instance.ts
@@ -269,7 +269,9 @@ t.test('CloudSQLInstance', async t => {
       await CloudSQLInstance.prototype.refresh.call(instance);
       instance.refresh = CloudSQLInstance.prototype.refresh;
     };
+
     await instance.forceRefresh();
+
     t.ok(
       cancelRefreshCalled,
       'should cancelRefresh current refresh cycle on force refresh'
@@ -290,7 +292,7 @@ t.test('CloudSQLInstance', async t => {
     let cancelRefreshCalled = false;
     let refreshCalled = false;
 
-    const refreshPromise = instance.refresh();
+    instance.refresh();
 
     instance.cancelRefresh = () => {
       cancelRefreshCalled = true;
@@ -302,13 +304,7 @@ t.test('CloudSQLInstance', async t => {
       return CloudSQLInstance.prototype.refresh.call(instance);
     };
 
-    const forceRefreshPromise = instance.forceRefresh();
-    t.strictSame(
-      refreshPromise,
-      forceRefreshPromise,
-      'forceRefresh should return same promise ref from initial refresh call'
-    );
-    await forceRefreshPromise;
+    await instance.forceRefresh();
 
     t.ok(
       !cancelRefreshCalled,
@@ -481,6 +477,43 @@ t.test('CloudSQLInstance', async t => {
     }
   );
 
+  t.test(
+    'close on established connection and ongoing failed cycle',
+    async t => {
+      let metadataCount = 0;
+      const failAndSlowFetcher = {
+        ...fetcher,
+        async getInstanceMetadata() {
+          await (() => new Promise(res => setTimeout(res, 50)))();
+          metadataCount++;
+          return fetcher.getInstanceMetadata();
+        },
+      };
+
+      const instance = new CloudSQLInstance({
+        ipType: IpAddressTypes.PUBLIC,
+        authType: AuthTypes.PASSWORD,
+        instanceConnectionName: 'my-project:us-east1:my-instance',
+        sqlAdminFetcher: failAndSlowFetcher,
+        limitRateInterval: 50,
+      });
+
+      await instance.refresh();
+      instance.setEstablishedConnection();
+
+      // starts a new refresh cycle but do not await on it
+      instance.close();
+      await instance.forceRefresh();
+      t.equal(metadataCount, 1, 'No refresh after close');
+
+      await t.rejects(
+        instance.refresh(),
+        'closed',
+        'Refresh after close rejected.'
+      );
+    }
+  );
+
   t.test(
     'get invalid certificate data while having a current valid',
     async t => {