Landlord and tenant lease renewal

Hey Guys, I own a rental property in Connecticut. I have this problematic tenant that I’m ready to get rid of. She never takes out her garbage on time, her son has costed me broken windows, I get noise complaints etc. In addition she is on section 8. Recently she said she had mice so I got an exterminator and when the exterminator came she refused to open the door. Not sure why but I tried my key to enter the apartment she changed the locks to my doors.

Long story short her lease is up October 31st, her case worker said I only have to give her 30 days notice but I want her out of there by the date the lease is up. Should I send her the non lease renewal notice In August so she has ample time to vacate the premise and find a new apartment. Or in September? Any thoughts ? I’m even concerned that she may damage my property beyond what her security. Can cover because she has such a bad attitude.

Thanks!