Electrical and optical spin injection efficiency of GaMnN/InGaN spin LEDs is evaluated. At room temperature, the spin LEDs are shown to exhibit negligible optical and electrical spin injection efficiency despite that the n-type GaMnN spin injector employed is ferromagnetic. On the other hand, carrier supply from GaMnN at low temperatures is accompanied by a reduction (by 1-5%) in optical polarization of the InGaN spin detector (SD) from its intrinsic values measured without carrier supply from GaMnN. This observation seems to indicate some degrees of spin injection from GaMnN with the spin orientation opposite to that of the lowest spin state of the SD. The very low degree of polarization, however, implies efficient spin loss during the spin injection process. From cw- and transient resonant optical orientation studies, the spin loss is attributed to fast spin relaxation within the InGaN spin detector.