There has been some changes since the OP asked this question and at least one relevant research paper has tried to provide a new answer to this question. According to study this (Mäntylä T. 2013) published in one of the top ten peer reviewed journal of psychology:
Yes there is evidence... but men seems better at it
(emphasis is from me)
The second main finding of Experiment 1 was that males (mean
proportion correct = .85) outperformed females (mean proportion
correct = .74) at multitasking, as indexed by accuracy in the counter
task, F(1, 70) = 6.25, ηp 2 = .08, p < .01.
As shown in Figure 1, the gender difference in accuracy favored men by about 10%
across the three counter tasks. This difference was not due to a trade-off
between accuracy in the counter tasks and in the background
(name-back) task, given that both men and women identified about 38%
of the targets in the name-back task (with no differences in false
alarms). Furthermore, gender differences in counter-task accuracy
were not related to differences in monitoring frequency (F < 1).
Females (mean proportion correct = .52) performed somewhat better than
men (mean proportion correct = .48) in the letter-memory task, but
this difference was not reliable (F < 1).
The second experiment demonstrated another interesting fact:
Experiment 2 provided additional support for this hypothesis by
showing that gender differences in multitasking (and spatial ability)
were eliminated among females who were in the menstrual, but not the
luteal, phase of their menstrual cycle.
The author is aware of some limit of his experiments. Most of them are related to the assumption that multitasking involve spatial abilities. I extracted the most interesting part of the discussion, but refer to the original paper for better understanding of their impacts. (again, emphasis is from me)
[...] it was necessary to use (gender-fair) test conditions in which
the role of domain-specific skills and experiences were minimized.
Furthermore, although most everyday multitasking may involve a great
deal of spatiotemporal processing, it is reasonable to assume that
these demands are domain specific. A central assumption of the
spatiotemporal hypothesis introduced here is that gender differences
in multitasking are expected when the demands on temporal coordination
are relatively high. In most dual-task conditions, these demands are
low and less dependent on spatial abilities than are multiple tasks
that may require coordination of a complex pattern of temporal
contingencies. This line of reasoning is also consistent with
evidence from earlier studies showing no gender-related differences in
[...] Another limitation of the study is that both experiments
involved relatively restricted time frames and predictable
target events (in the counter tasks). The term multitasking is a
loosely defined construct that covers a wide spectrum of activities
and time frames. Multitasking in some conditions may require very
narrow deadlines (e.g., air traffic control), whereas other types of
multitasking (e.g., household activities) may impose lower demands
on spatiotemporal processing because of more-generous time windows.
It is reasonable to assume that, like most goal-directed tasks,
everyday multitasking reflects different mixtures of task-independent
cognitive functions (e.g., components of executive functioning and
spatial processing) and more domain-specific skills and strategies.
From this perspective, individual differences in multitasking should
be considered in relative terms, given that some conditions may show
reduced or even reversed gender differences because of task-specific
constraints and strategies.
Mäntylä T., Gender Differences in Multitasking Reflect Spatial Ability,
Psychological Science, April 1, 2013 24: 514-520