Edit: Now there's some evidence for this idea
I thought I'd come back to this question, because I wasn't really satisfied with what the literature yielded back then and the paper that Peters mentioned (there had only been a press release) has come out.
Stoet, O'Connor, Conner, & Laws (2013) looked at this and found some evidence for the idea.
Quoting from their abstract
Background
There seems to be a common belief that women are better in
multi-tasking than men, but there is practically no scientific
research on this topic. Here, we tested whether women have better
multi-tasking skills than men.
Methods
In Experiment 1, we compared performance of 120 women and 120
men in a computer-based task-switching paradigm. In Experiment 2, we
compared a different group of 47 women and 47 men on
"paper-and-pencil" multi-tasking tests.
Results
In Experiment 1, both men and women performed more slowly when
two tasks were rapidly interleaved than when the two tasks were
performed separately. Importantly, this slow down was significantly
larger in the male participants (Cohen’s d = 0.27). In an everyday
multi-tasking scenario (Experiment 2), men and women did not differ
significantly at solving simple arithmetic problems, searching for
restaurants on a map, or answering general knowledge questions on the
phone, but women were significantly better at devising strategies for
locating a lost key (Cohen’s d = 0.49).
Conclusions
Women outperform men in these multi-tasking paradigms, but
the near lack of empirical studies on gender differences in
multitasking should caution against making strong generalisations.
Instead, we hope that other researchers will aim to replicate and
elaborate on our findings.
--- end edit
Old answer
No, there is no such evidence.
Apparently there didn't use to be much evidence against it either, but I found two recent studies by Noemi Peters (2010, 2011).
First I did a search on "sex
differences" multitasking and similar
terms, but I could only find a dodgy
study in support and not much
well-received publications in the
field anyway. Apparently Ms Peters found the
same dearth in the literature. The fun part:
I found her publications by looking who had
cited the Pease book :-)
I searched extensively for peer-reviewed scientific publications that
examine gender differences in multitasking ability, but the closest I
could find is Criss (2006) and Havel (2004), which are manuscripts that
are made available online at the website of the National
Undergraduate Research Clearinghouse. Both examined subjects who had
to perform some specified tasks while tallying keywords from a
song/story.
None of them found gender differences in productivity when multitasking, but Criss (2006) found that women were better at
accuracy. Nonetheless, we do not know whether the findings can be
attributed to multitasking as none of them had a control
group. Besides, some British newspapers reported recently about an
experiment that supports the view that women are better (see Gray,
2010), but when I contacted the lead researcher, Professor Keith Laws,
it turned out that there is not even a working paper yet that I could
discuss here.
Her evidence to the contrary wasn't published
in peer reviewed journals, so if somebody
has something stronger, better pay attention to that instead.
From the abstract of her dissertation:
The view that women are
better at multitasking is widely held,
however there is no scientific
evidence supporting it. This
experiment examines whether there are
gender differences in multitasking
ability and in the inclination to
multitask. To this end, I conduct an
experiment with three treatments: one
where subjects have to execute two
tasks sequentially, one where subjects
are forced to multitask with the two
tasks, and one where they can choose
freely how to organize their work.
The results of the third treatment
indicate that there is no gender
difference in the inclination to
multitask. As far as multitasking
ability is concerned, I do find a
gender difference but it is contrary
to the widely held beliefs: point
estimates indicate that men perform
better both under forced and voluntary
multitasking. This gender difference
reaches statistical significance in
case of voluntary multitasking.