Provided the property was advertised and/or your intent to rent it again was up until at least the date you signed the sales contract to commit to the closing, you're fine claiming valid expenses on the SCH E.
Now for property improvements, you enter those in the assets/depreciation section, as those are added to your cost basis. Make the in service date for property improvements done after the last tenant moved out, the closing date of your sale. That way no depreciation will be taken, or if any is taken it will be to minuscule to matter or make any difference.
