It depends on the rules used which are not consistent, perhaps vague, or non existent.  However, this is not a throwing rule, it is a record's rules/issue.  

An example of what was done in KC for Mike Zolkiewicz's weight over bar record.  The bar was level as they knew a record attempt was about to be made.  After the attempt, Kevin Henderson took an extra tape measure tossed it over the bar and measured in the middle directly under the bar. The tape was pulled taut and it measured twice the distance confirming the uprights tapes.  The reading of the extra tape was confirmed by the judge and the AD and witnessed by several other judges who stopped to watch this feat. 

The ground was a bit chewed up;  The mark was not generous, perhaps a bit onerous as he was standing in a slight depression made by the previous throwers --- However it was by the rules without picking a spot to generate the desired distance.

NASGA General Rules for Height Event #6: All measurements will be made from the ground to the top of the crossbar.

USAD & Borges I.3.e. All measurements shall be made from the ground to the top of the crossbar at its lowest point.

SSAAA and RMSA #6.  All measurements will be made from the ground to the top of the crossbar at the center of the crossbar.

USAD and NASGA -  When an American, North American, or World Record has been broken it is the responsibility of the Judge or Athletic Director to verify that record. The Record must be set within all rules for that event. The implement will be weighed on a certified scale and the weight will be equal to or more than the legal weight for that implement. In the case of the Weights for Distance, the Weight for Height, and the Hammer Throw, the overall length of the implement will be measured and the length will be equal to or less than the legal length of that implement.

RMSA - When an American, North American, or World Record has been broken it is the responsibility of the Judge AND Athletic Director to verify that record. The record must be set within all rules for that event. The implement will be weighed on a certified scale and the weight will be equal to or more than the legal weight for that implement. In the case of the Weights for Distance, the Weight for Height, and the Hammer Throw, the overall length of the implement will be measured and the length will be equal to or less than the legal length of that implement. (Measure for records on height events by measuring with tape on each end of the bar and from the center of the bar.)

Borges Rules - I do not believe his rules mentions anything about measuring for records.

Wayne Hill wrote: The point is that you believe the throw was good and have done due diligence to certify the weight.

I would add the following:

Since there is no definitive rule stating you must measure in the middle to submit a record, you could avoid it but I suppose some may question the legitimize.

If no center measure, then I would ask myself the following:

• Is the ground level & flat?,
• Is the bar level?
• Does the bar sag? 
• Is the marks on my uprights for the measuring tape accurately?
• Did the tapes on the side towers get double checked?
• After the throw, was the measure double checked at the towers?

a random thought: Although the distance by which a record is broken should not effect your procedure, it might.  If the record falls by a foot or by an inch, would you do the same thing?

Another plus side to the pole vault bars ... if one side lets loose, and the bar swings like a pendalumn, it won't do anywhere near the harm that a steel bar could do