Why don't you want us to contact the hiring authority for a particular job I previously had?

Do you mean that someone might ask you why you don't want THEM to contact the hiring authority for a job YOU once held?

Depends on why you don't want the authority contacted.

Bad work performance, personality differences, job ended, something else?

I would allow the prior employer to be contacted. Are you in the US? If so the former employer would be foolish not to just list your dates of employment and the fact that you no longer work there. Otherwise, they could be sued.

Thanks, I know I could sue but I would never know what was said. It is a gov't job I lost and gov't job I am applying for and Im afraid they may communicate a little more with one another and give more information than I'd like and I would never know if that's why I didn't get the job or not, am I making sense?