Microsoft Teams default behavior is to allow access files only to those who are part of a specific Team, whether they are owners, members or guests.
That doesn't mean you can't share files across departments without avoiding creating another copy for it, but you'll need to do a couple extra steps to allow this:
1. While on your Team and Channel Files section where the file is located, click on Open in Sharepoint. This will open your default web browser and, if you haven't logged into Office 365 there yet, you will be prompted to do so.
2. Once logged in, you will see the back-end that manages your Team's files. Look for the file you'd like to share and click on the Share Icon.
3. On the next step you have to decide how much you want to restrict the access to the file.
Allow editing will give the recipient rights to modify the file, do not enable this if you mean the file to be read-only.
For deciding who will be able to access the file:
People in City of Worthington with the link will do exactly what it says, anybody in the City could receive a copy of the link and access the file.
Specific People is usually the recommended approach as you control who can access the document and avoids them for forwarding the file link to someone else.
Anyone with the link is the least restrictive option. This allows for people even outside of the organization to be forwarded a link to the file. This is the least recommended approach as you lose control of who is accessing the file.
4. Once you've selected your options above, you'll have to choose the email recipients that will receive the file link. I recommend that you disregard using the Copy Link and Outlook options before choosing your recipients and clicking Send. The reason is that otherwise you wouldn't be applying the permissions to the people you want, and you might find that multiple email requests for access are sent to all of the Team owners every time that another person tries to open the document.
Using this dialog allows you to choose multiple recipients and include a description that will be sent to them in the body of the automated email from Office 365.
5. A confirmation will show on screen after clicking Send. This completes how to share the file.