I requested TurboTax to file my city tax return in addition to federal and state. City states it did not receive. how do I check to see if it was filed and get a copy

First see this FAQ about which city returns TurboTax can prepare and which ones can be efiled or have to be printed, signed, dated, and mailed.

FAQ:  Which city tax returns can I do in the TurboTax state program?

https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/city-tax-returns-turbotax-state-program/L0fev7XS3_US_en_US

If you need more info, please specify the city and state, and someone familiar with your city may comment further.

ADDENDUM

@rpcation  wrote:  "How do I check to see if it was filed and get a copy"

If you used Online TurboTax here's how to get a copy.  It should be in your return PDF following the state return.  But here's a way to get the larger PDF available inside your return's Print Center that includes the Federal, state and city returns and worksheets.   Each return should also have a page called "Filing Instructions."

NOTE:  When you open the return interview, do NOT make any changes.  If you ever need to formally amend the return, it has to start off exactly like it was when originally filed.

• Log in and at the Tax Home page look for a link "Add a State."  That doesn't really add one, but opens the return interview.
• After the return interview is open, click in the left menu column on TAX TOOLS, then PRINT CENTER.
• Then choose "Print, save, view this year's return."
• The next screen should offer some options:  "Just my tax returns", or "include government worksheets (optional)", or "include government and TurboTax worksheets (optional.)"
•  The latter has the most pages.

NOTE:  Remember all PDF tax documents and tax data files are very sensitive files, since they contain your personal ID info, financial data, and possibly bank account numbers, etc.  Be sure to store them safely and securely to guard against computer theft, hacking, etc.