ARS 28-1388 requires that a physician or another qualified person draw blood for police purposes. The person tested must also be given a chance to have someone of their choice carry out additional test(s). The law also provides that even if blood is drawn from a person for some reason other than determining alcohol or drug levels, a sample must be provided to police if requested.
A person or hospital may not be sued for collecting blood or urine in relation to a DUI arrest, unless they are seriously careless. An situation where a hospital may be sued could be where the hospital uses unclean supplies and infects a person with some disease.
If when under caution or arrest you refuse or resist blood or breath tests, which may be used as evidence against you at trial, then you could be charged with an additional class 1 misdemeanor.
In the state of Arizona, this can result in up to 6 months in jail, which a judge may require you to serve the entirety of before release. You may also face a fine of up to, but not exceeding $2,500.