I found that the "client_modified" of a file was not updated if the file is already exists on Dropbox.
API: https://www.dropbox.com/developers/documentation/http/documentation#files-upload
This is my test steps (using HTTP request)
1. upload a file (with client_modified)
// the client_modifed was updated
2. upload the same file (with only client_modified time changed)
// the client_modified was NOT updated
You can get the same results from API explorer
https://dropbox.github.io/dropbox-api-v2-explorer/#files_upload