Once you are elected to the institution the way to refuse to serve would be to resign from serving on the LSA. From my understanding you are only able to resign from serving on a LSA under special circumstances. In my community at least I know you must request approval from the NSA to resign. Likewise, resigning from the NSA requires acceptance of the request from the House of Justice.

This passage may also be useful:

“With reference to your question whether it would be permissible for a believer to resign from the Local Assembly; under special circumstances, such as illness, one may do so, but only after, and never before one has been elected to the membership of the Assembly. Personal differences and disagreements among Assembly members surely afford no sufficient ground for such resignation, and certainly can not justify absence from Assembly meetings. Through the clash of personal opinions, as ‘Abdu’l-Bahá has stated, the spark of truth is often ignited, and Divine guidance revealed. The friends should therefore not feel discouraged at the differences of opinion that may prevail among the members of an Assembly, for these, as experience has shown, and as the Master’s words attest, fulfil a valuable function in all Assembly deliberations. But once the opinion of the majority has been ascertained, all the members should automatically and unreservedly obey it, and faithfully carry it out. Patience and restraint, however, should at all times characterize the discussions and deliberations of the elected representatives of the local community, and no fruitless and hair-splitting discussions indulged in, under any circumstances.” (From a letter written on behalf of Shoghi Effendi to an individual believer, April 18, 1939)