Yes. And not just by the police.
There are existing demonstrated attacks which allow a malicious 3rd party to do so.
At the RSA conference, there was a particularly scary session called Hacking Exposed: Mobile RAT Edition. CrowdStrike co-founder Dmitri Alperovitch showed an end-to-end targeted attack on an Android smartphone, starting with social engineering to trick the user into clicking a link, silently installing malware via a drive-by download, and then covertly taking control of the device, accessing the microphone and camera, to steal sensitive information.
Do you have any apps that let you open links inside them without having to go to your browser app? The component that renders the page for you in that situation is called Webview – and if you are one of the 950 million people who are running Android 4.3 Jellybean or lower, you need to know about this vulnerability.
Google has no plans to patch this vulnerability in Android 4.3 or lower.
Another example would be Carrier IQ which came installed on 150 million phones (by the manufacturers or network operator) which was shown (depending on what settings the carrier chose) to send every keypress in plaintext over the network, including usernames and passwords.
So, apps can listen in on you and apps can send info to 3rd parties. Now lets give an example of remote installation.
Google includes a nice feature which is very convenient for user but is only possible because they have the absolute power to install apps remotely without interaction being required on the phone:
Launch the Google Play Website on your PC or any other device that you’re using. Sign in with your Google account from the menu in the top right. Make sure that you sign in with the same ID that you use on your Android phone.
Browse through the Google Play store in order to find the app that you’re looking for. You can view the apps in categories and can also search for the app through the search text box. Once you find the app that you’re looking for, click on it. You’ll be taken to the app’s download page.
Tap on the Install button below the app name. You’ll now see an app installation popup with details, such as the app’s permissions.
Click on the dropdown menu below Choose a device and select your Android phone. Click on the INSTALL button.
You’ll now get a Congratulations popup message. Click on the OK button. That’s it! The app will now be installed on your phone if your device is connected to the internet. If the device is not connected to the internet, then the app will be installed as soon as there is an internet connection.
Since you can do this from your google account page it's a simple demonstration that google can do this at any time with arbitrary applications. If a court orders them to give someone access to the "install applications remotely" page for your devices then do you think they're going to refuse?