Then a blood test of the thyroid functions (TSH and maybe thyroid hormones T3, T4) should be considered. This will normally be done within a routine check of the patient.
If the patient (or family) has a history of seizure the doctor will do an EEG. This will not show specific signs of ADHD but might exclude specific forms of seizures. If the doctor and you decide to use psychopharmacological treatment an EKG should exclude significant heart problems.
A scull X-ray (Computer tomography, NMR) can be useful to exclude rare other causes of attention problems (like malformations of blood vessels, tumour, hydrocephalus). But these are very rare conditions!
Some parents think very specific diagnosis of functional imaging (SPECT, PET) will show specific signs of ADHD. At the moment these diagnostic tools are mainly used for research. You have to consider possible side effects of nuclear medicine especially for children. So these diagnostic tools cannot be recommended for a routine diagnosis of ADHD.