This paper considers a special class $$S_{L}(h)$$
S
L
(
h
)
of logharmonic mappings of the form $$f(z)=h(z)\overline{h^{\prime }(z)},$$
f
(
z
)
=
h
(
z
)
h
′
(
z
)
¯
,
where h is analytic in the unit disk U, normalized by $$h(0)=0$$
h
(
0
)
=
0
, $$h^{\prime }(0)=1$$
h
′
(
0
)
=
1
, and h(U) is starlike. For this class of functions, a distortion theorem is proved, and Bohr’s inequality along with some improvements and refinements is investigated. In addition, the radius of starlikeness and an estimate for arclength are obtained.