Whether your criminal record will affect your application depends on the severity of your offence as well as the specific course that you are applying for.
For example if you have been involved in a petty crime (e.g. shoplifting, trespassing), the university may gloss over your criminal history.
If you are considering programs that involve interaction with people, especially the young or vulnerable (e.g. Nursing, Education), your crime will be more closely scrutinised.
We advise that you declare all criminal records (both local and overseas) in your university application. Ultimately, you may be asked by the university to provide a police criminal record as part of your enrolment requirement.
Your records may also be checked by the immigration authority when you apply for your student visa.
So our advice for you is to declare any records that you have upfront and early.