Mrs May - who is also the town's constituency MP - has made the plea.
Maidenhead's own mayoral chain and mace was taken out of use in 1974 when the town was combined with Windsor to form the Royal Borough - Windsor's own official regalia being promptly adopted as the official one for the new borough.
The decision has rankled with many Maidenhead people over the years. Now Mrs May has called for the Maidenhead chain and mace to be reinstated alongside the Windsor ones, so that both can be used.
Last year's mayor Cllr Colin Rayner was the first to make a protest - by resolutely wearing the Maidenhead chain at several events in the town, its first outing for several decades.
Mrs May believes there is no reason for the Windsor regalia to take precedence and has written to the leader of the council Cllr David Burbage, to ask him to consider this.
Mrs May wants the Maidenhead chain and mace reinstated on an equal basis to the Windsor ones, with the Mayor choosing which to use on which occasion.
She said: "This would be a symbolic change, demonstrating Windsor and Maidenhead’s equal status within the Royal Borough.
"The Maidenhead regalia are of historic importance and it would be greatly welcome if the council could demonstrate that it understands the traditions and history of Maidenhead in this regard.”
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The Met Office has issued a yellow alert for Windsor and Maidenhead, Slough and Wokingham, warning that rain moving eastwards across the south of the country may turn to snow in some places.