Error: When I wrote this up I, I had misread the question and focused my answer on the office of Deacon. I will need to revise this to focus on the office of Elder. It won't be substantially different but there are a few extra considerations.
There is not a very clear answer to this question, but the statement on the CBE seems to beyond the scope of documentation coming from the EFCA itself.
The terminology used in the EFCA is a little bit confusing. You have the common monikers of "Ordination", "Elder" and "Deacon", but you also have the terminology of "Credentialing" (not at all the same as "Licensure" in Reformed circles) and various forms of "ministry" that have qualifications but do not require ordination.
Relevant to this issue is something the EFCA calls a Certificate of Christian Ministry:
The primary purpose of the Certificate of Christian Ministry (CCM) is to identify theological proficiency. (This expands on the License, which focuses on theological competency and alignment with the EFCA, and is distinguished from the Certificate of Ordination, which focuses on theological mastery.)
(source: Certificate of Christian Ministry, 2008 EFCA Statement of Faith)
This so called CCM can be issued to both men and women:
Who can be credentialed? Can a woman be credentialed?
Any who are in a qualifying ministry and fulfill the requirements as stated in “Steps” can be credentialed. This means women serving in local church staff positions can receive the Certificate of Christian Ministry. (The Certificate of Ordination is reserved for men who are qualified, as the EFCA Conference determined our national credentialing process would be complementarian.) Because of the importance of credentialing to the local church ministry and the EFCA, all women serving in qualifying ministries ought to be encouraged to be credentialed.
(source: EFCA Credentialing FAQ)
This is distinct from a Certificate of Ordination which only men may hold:
The ordination credential may be issued to candidates who:
(source: Credentialing: Certificate of Ordination)
So far those procedures are pretty standardized. The remaining question is what kind of certification is necessary to hold the office of deacon. This is where things get foggy. Is a Certificate of Christian Ministry enough or must one be Ordained?
The answer is, unfortunately, you don't actually need either, although the former is highly encouraged. EFCA churches are considered to be somewhat autonomous and each have their own constitution. You can see in the sample constitution that what offices a local church even consists of is something that a local church could amend. They are encouraged to change as little as possible here, but that doesn't mean that all local churches will have the same church governance structure. The exact role of Deacons is notably not well defined by the denomination.
The EFCA lumps Deacons in as part of the "Church Board" responsible for governance of the church (along with the Pastor and Elders), but they also draw a distinction between them, often citing "Elders/Overseers/Pastors" as one thing and "Deacons" as something different (along with different verses used to define their qualifications).
Likewise strange to me, EFCA churches often allow non credentialed people into ministry roles (including holding titles of Pastor and Elder) before having completed (or even without) their credentialing process.
One hint can be found in the Credentialing FAQ cited above (emphasis mine):
Scripture clearly teaches that each believer has been given a grace-gift in order to serve our Lord and His Church. In addition, some believers have received the call of God upon their lives for vocational ministry and have been given grace-gifts for the task of preparing God’s people to carry out the works of service which build up the body of Christ. It is those in vocational
ministry which God Himself has chosen and appointed and which the local church affirms, and is subsequently recognized by the EFCA by the act of the laying on of hands and the granting of an EFCA credential.
In other words the credentialing process can be done post hoc in recognition of those already called to vocational ministry. This may or may not include Elders, much less Deacons. Local churches are encouraged to have their ministry staff pursue the credentialing process, but it is not necessarily a given. In particular, the requirements for credentialing define vocational ministry as at least 30 hours a week of compensated ministry time. Exceptions are made particularly for bi-vocational ministers because the importance of the credentialing process is stressed over other particulars, but the fact remains that it is not a strict requirement at all unless the local church makes it so.
In short, you cannot learn whether a woman may serve as a deacon in an EFCA church based on any ordination or certification requirements. The certification requirements are valid for woman, and neither ordination or certification is actually required. The ordination process is for men only, but according to denomination minimum standards a woman could serve with the title of "youth pastor" and receive a Certificate of Christian Ministry rather than a Certificate of Ordination.
It seems quite likely to me that any given local congregation might be confused on the exact difference between ordination and certification. A deacon might be hold a certificate of ministry and installed by the local church but that isn't actually the formal definition of ordination.
One can definitely say that according to EFCA standards those ordained for Ministry of the Word, especially to include lead Pastors, must be of the male persuasion. This is traditionally understood to also include Elders (who may be ordained if ministry roles call for it but are at least encouraged to hold a Certificate of Christian Ministry). On the other hand woman are clearly allowed to hold a CCM and participate in staff positions including vocational ministry, even hold the title of Pastor (in the context or Youth Pastor, Counseling Pastor or other administrative roles) but not that of a Lead Pastor. Whether the office of Deacon is seen as part of a Ministry of the Word and thus limited to men or whether it includes other acts of ministry is something decided on by the local church and hence their gender requirements may vary.