Yes, a urinalysis should help you determine if there is something to be concerned about.
In addition to a UTI or spay incontinence, there can be other things that a urine sample can rule out (crystals in the urine, abnormal cells, protein, etc).
I have also had some patients that will have what is called overflow incontinence. That is when they, presumably, drink a lot of water just before bed time. Their bladders get so full, and they just can't hold it in. It is different that spay incontinence in that with the "spay incontinence", the sphincter just needs a little more hormone to keep working. In overflow incontinence, it is NOT a hormonal problem so much as a "I drank too much water before I went nighty night" problem.
I would start with a urinalysis and go from there, as everyone suggested.