Garda tests on a tyre of Dana's presidential campaign car show no evidence of criminal damage.
However, a further examination will now be carried out by the tyre manufacturer, Michelin.
It is understood Michelin will be able to strip layers of rubber off the side wall of the tyre to assess whether it had been interfered with.
Police in the Republic are satisfied, however, that the blow-out on the M4 motorway, near Kilcock, Co Kildare, last week was caused by driving a lengthy distance after the tyre had been punctured.
The Londonderry native's husband, Damien Scallon had claimed the tyre was deliberately damaged and reported the incident to the gardai.
He alleged that somebody was trying to "injure us or murder us".
The damage is believed to have resulted from the side of the tyre being trapped between the rim of the wheel and the road.