Can someone being accused to be the father of a child refuse a DNA test?

Yes.

Generally yes, until you are served with a summons and court order for DNA testing, at which time you must submit to testing or face sanctions, which could include but not be limited to being held in contempt of court, a writ of bodily attachment, a default being entered against you, or incarceration. Consult with an attorney to discuss the specifics of your situation and your options.