Short answer. No. The Rules of Court let the court arrest a party for disobeying most discovery orders, but it expressly carves out an order to submit to a physical or mental examination from that arrest power. Refusing that specific kind of order can still bring other consequences, just not arrest.
What the law says
In lieu of any of the foregoing orders or in addition thereto, an order directing the arrest of any party or agent of a party for disobeying any of such orders except an order to submit to a physical or mental examination.
Rule 29, Section 3 — Other consequences. Read the full provision →
What this rule covers
Rule 29, Section 3 of the Rules of Court deals with a party who refuses to obey an order compelling him to answer questions, produce documents, allow entry upon property, or submit to a physical or mental examination under Rule 28. When that kind of disobedience happens, the court may issue several kinds of orders in response, ranging from treating disputed facts as established, to barring the disobedient party from presenting certain evidence, to striking pleadings, staying the case, or entering judgment by default against him.
The arrest option, and its explicit carve-out
One of the consequences the rule authorizes, in place of or in addition to the others, is "an order directing the arrest of any party or agent of a party for disobeying any of such orders except an order to submit to a physical or mental examination." That exception is unambiguous: arrest is available for disobeying the other kinds of discovery orders the rule lists, such as an order to answer questions or produce documents, but it is specifically withheld where the disobeyed order was one requiring a physical or mental examination.
Why the exception exists for this order
A physical or mental examination involves submitting your own body or mind to an outside evaluation, which is a more personal intrusion than producing a document or answering a question. The rule's drafters singled this order out from the arrest remedy, leaving the other consequences the section lists, such as treating your condition as established against you, or barring you from introducing evidence of your physical or mental state, as the available responses to a refusal instead of jailing you over it.
Refusing still has real consequences
This exception does not mean refusing the examination is consequence-free. The court can still order that your physical or mental condition, or the facts the examination would have addressed, be taken as established for purposes of the case in line with the other party's claim. It can also bar you from opposing designated claims or from introducing your own evidence about your physical or mental condition, or, in a fitting case, strike your pleadings or enter judgment against you. Arrest is simply not one of the tools available for this particular kind of order.